HEAT TRANSFER MODELING OF A DIESEL ENGINE
The solution of heat transfer phenomena in Internal Combustion Engines is a very
challenging task considering the number of systems (intake and exhaust ports, coolant
subsystem, lubricant oil subsystem), the different heat transfer mechanisms (convection,
conduction and radiation) and the quick and unsteady changes inside the cylinder that take
place at the same time. These difficulties had led to a lot of experimental and theoretical
work over the last years. A review of these works can be found in Borman and Nishiwaki
[1], and Robinson [2].
Several authors [3-6] have documented the relevance of the understanding of heat transfer
phenomena at the earlier stages of engine design, when the thermal endurance and stability
of the composing combustion chamber parts have to be assured. Since engine efficiency
and emissions are affected by the magnitude of engine heat transfer, which is directly
related to the magnitude of combustion chamber wall temperatures [7-13], it is also during
the design stage, that the strategies to control these temperatures, as well as heat and mass
transfer involved in the engine cooling system, especially during cold start and transient
regimes, must be envisaged. Among others, coolant temperature control is being considered
as part of various technology solutions to control material temperatures, given the linear
dependency between them [5, 14].
The definition of the requirements for the coolant temperature control and the engine
control strategies require detailed knowledge about the thermal engine behaviour. So, an
accurate prediction of the metal temperatures and heat flows through the cylinder head,
piston and the cylinder liner boundaries is important to engine design, performance
prediction and engine diagnosis.
Aforementioned explains the continuous work on engine heat transfer and thermal
management carried out by many research groups. In the framework of a research program
concerning heat transfer in Diesel engines, the authors [5, 6] already discussed the
convenience of using a reduced thermal model for calculating the cylinder head, piston and
liner temperature, while conducting combustion analysis. The aim of the present work is to
improve the thermal resolution of the mentioned model, and also to extend its capabilities
in order to incorporate it into a more comprehensive engine thermal management model.
The developed tool can be used in the modelling of different cooling system architectures to
assess their impact on oil, coolant and metal temperature, thus saving on extensive and
time consuming test work. With this aim the following procedure has been chosen:
1. A more detailed partitioning of the engine geometry into nodes, without loosing the
functionality and readiness of the program that characterize the concise wall temperature
predictive model reported in [13].
2. The assessment of engine energy balances, as well as the rate of heat rejection to the
coolant system.
As a result, in addition to the calculation of metal temperatures, the thermal model allows
the calculation of the heat fluxes through combustion chamber elements (in which the
engine enclosure has been divided) and engine boundaries and, in particular, with the
calibrated engine predictive thermal model it can be estimated the engine heat rejection to
the coolant.
The presentation of the work is organized as follows: first, a brief description of the
electrical equivalent model of the engine is explained, including a brief explanation of the
combustion chamber nodes. After that, the modelling of the boundary conditions is treated,
that is: the model of heat transfer between the in-cylinder gases and combustion chamber
walls; between the gas and the intake/exhaust runners; between the coolant and the liner
and cylinder head; between the oil and the piston; between the oil and the liner; between the
piston and the liner. Then, a short explanation of the model code is described, followed by a
comparison between experimental and model results. Finally, the main conclusions of this
work are given.
2. THE THERMAL MODEL.
The thermal model developed has been adjusted by means of a thorough experimental work
on a specific four cylinder Diesel engine, in which its first cylinder was isolated from the
other three and instrumented with 23 thermocouples in the cylinder liner, 16 thermocouples
in the cylinder head, and 2 thermocouples in the piston (a detailed description of the set-up
can be found in [16]. The main characteristics of this engine are given on table 1.
Table 1: Engine main characteristics
Stroke
80 mm
Bore
75 mm
Maximum BMEP
1,96 MPa
Nominal speed
2000 rpm
The model is a lumped parameter based on the electrical analogy as performed by other
authors [18, 19, 20]. In this kind of models, the engine is treated as a thermal network
formed by a finite number of physical nodes considered to be isothermal (resulted from an
accurate geometrical discretization of components), linked by means of thermal resistors
representative of thermal conductances. Nodes can be either capacitance nodes, possessing
mass, or convective boundary nodes with specifying temperature. The heat in the network
is transmitted from the source terms to the heat sink nodes through thermal resistors
(convection or conduction resistors) with a dynamics dictated by the network topology and
lumped capacitances.
To meet the correspondence between the actual system and its electrical analogous, engine
piston, cylinder head and cylinder liner have been divided into elementary geometrical
pieces (nodes) in accordance to the number of temperature sensors installed to
experimentally validate the model, and taking care of meeting the Biot number criterion (to
assure that the temperature is uniform over the node).
2.1. The FE model.
The models of the cylinder head, liner and piston were created by using a commercial 3D
software. This allowed splitting these complex components into small parts and getting the
mechanical characteristics such as connecting areas, distances between centres of mass, and
masses of elements. Valves and injector were also decomposed into smaller parts. The
cylinder liner was divided in the axial, circumferential and radial direction as shown in
figure 1. The fact that only three quarters of the piston stroke was cooled was also taken
into account. In total the cylinder liner is made up of 51 cylinder nodes. The nodes at the
inside are connected with the piston through the segments.
Figure 1. Cylinder liner decomposition
Figure 2. Piston decomposition
The piston was divided in 6 nodes. In figure 2 the referred nodes are, from top to
bottom, the bowl centre, the bowl rim, the piston crown, the piston centre, the ring
waist housing the oil cooling gallery, and the piston skirt. With the contact area and
the distance between the nodes, the conductances between them could be calculated.
An axisymmetric temperature distribution was assumed for the piston and liner.
The CAD model of the cylinder head is represented in figure 3. It consists on fire deck,
exhaust and intake runners and valves with their guides and the injector. All these elements
are separated in two different parts: lower and upper. The cylinder head model was divided
into 35 nodes. Because of the special interest the fire deck of the cylinder head, it was
modelled in more detail. The partition is shown in figure 4.
Figure 3. CAD model of the structural part of Figure 4. Cylinder head decomposition
cylinder head corresponding to one cylinder.
2.2. Interactions and boundary conditions.
Thermal calculations include the determination of heat fluxes from in-cylinder gases to
combustion chamber walls, the heat fluxes through the metallic parts, the convection from
the intake and exhaust gases around the surfaces of valve stems, inner surfaces of valve
seats and along the intake and exhaust port walls, and also the convection from the metallic
parts to the cooling and lubricating oil media. Although the heat fluxes in combustion
chamber have a periodically changing nature in time, the analysis is made assuming steady
state loading using the cycle averaged values. This assumption is reasonable considering
the speed of the periodical changes as compared to thermal inertia of all the components of
cylinder head, piston and liner. The same assumption is valid for the exhaust and intake
gases. Thermal contact interactions between valves and valve seats are described by heat
flux q AB from the solid face A to B, which is related to the difference of their surface
temperatures TA and TB , according to q AB  k TB  TA  , where k is the contact heattransfer coefficient.
Basic principles of nodal model.
For each component, the boundary conditions are specified, either by media (coolant, oil,
etc.) temperature and heat transfer coefficient from the outside wall surface to the media, or
by specified wall temperature on outside surface. In the model each node is connected to
other nodes and boundary conditions. Once the structure is divided into nodes, the energy
conservation equation can be written for each node. The sum of heat fluxes between nodes,
convective heat fluxes and other heat fluxes in a time span t equals the change in sensible
energy of the node (eq. 1).
mi cv
Tt i t  Tt i
  Kij Tt j t  Tt i t   qk i   hli Ali Tl  Tt i t
t
j
k
l




(1)
With mi the mass of node i , cv its heat capacity, K ij the conductance between node i
and a node j , hli the heat transfer coefficient between node i and a boundary l and
Ali the corresponding contact area. At the right side the temperatures at the instant
t  t are used (the implicit formulation). The advantage of the implicit formulation is
that the solution is unconditionally stable when simulating transitory behaviour.
Because the model described here was also used for transitory calculations the
implicit form was used.
For each of the n nodes of the model there is an equation like equation 1, forming a
system of n equations and n unknown node temperatures. Equation 1 gives rise to a
set of linearized, implicit equations of the form:
C  T   Q  C  T   H 

 K  
t  t
t
t 
t

(2)
Where, K  and C  are n  n conductance and capacitance matrixes, respectively. The
ith diagonal element of the conductance matrix is the sum of all the conductive and
convective conductances to node i. The element on the ith row and jth column is the
conductance between nodes i and j with a minus sign.
K ij 
K ij 
K
ij
j
  hli Ali
if
i j
if
i j
l
 K ij
(3)
Tt  and Tt t  are column vectors of n elements with the old and new temperatures of
the nodes. Q is a column vector with the sum of the heat fluxes to node i on the ith
row. This can be e.g. a heat flux generated by friction. H  is a column vector with the
ith row the sum of the product terms Tl hli Ali for the convective boundary conditions of
node i .
For stationary conditions, nodal thermal masses are not included in the equation 2,
Tt i t  Tt i , and equation 1 reduces to:
K  T   Q  H 
(4)
The assembly of the equations (2) and (4) is performed automatically based on general
engine specifications and is solved implicitly for the temperature vector T  ,
employing a Gaussian elimination procedure.
Modelling the boundary conditions.
The model to predict the temperatures of the metal parts, results in a thermal resistor
network made up of 92 metallic nodes and 8 convective nodes, which represent the
boundary conditions, characterized by their instantaneous media temperatures and film
coefficients.
The conductances between the combustion chamber nodes and oil/coolant flows have been
determined assuming that they depend on the boundary flows or the piston speed in a form
like




1
Exp _ i  j 1
1
Ki j  Kconst
 Ci j x 
(5)
With x representing the coolant flow or the piston speed, Ci  j is a multiplicative factor and
Exp _ i  j is an exponent to be fitted. Kconst is a constant conductance. K i  j is the series
configuration of Kconst and the variable-dependent conductance. All conductances of the
model are discussed in detail in the following paragraph.
Boundary condition between the gas and combustion chamber walls.
The changing nature of intake, in-cylinder and exhaust processes reflects in a change
of the boundary conditions. To predict the mean wall temperatures during the engine
working cycle, heat flows have to be calculated using cycle averaged boundary
conditions. The mean heat flux ( q ) between the gas and a wall permanently in contact
with the gas (e.g. piston, cylinder head) is found integrating the i nstantaneous flux
q  over a cycle.
720
1
1
q
q d 

720 0
720
 h T    T d
720
gas
wall
(6)
0
With h  the instantaneous heat transfer coefficient as function of crank
angle, Tgas   the instantaneous gas temperature and Twall the combustion chamber
wall temperature.
Introducing a mean film coefficient ( h ) and an apparent gas temperature ( T gas ):
720
h
1
h .d
720 0
(7)
720
T gas
1
Tgas  h .d
720 0

h
(8)
The mean heat flux can be written as:
q  hT gas  Twall 
(9)
So, the conductance between each of the nodes (piston and cylinder head) in contact
with the in-cylinder gases is calculated as the product of this mean film coefficient
times the area, K gasi  Agas,i  hg . The apparent gas temperature ( Tgas ) is used as
boundary condition.
The conductance between the in-cylinder gases and the internal nodes of the cylinder
has been calculated bearing in mind that they are not in contact along all the cycle . So,
apparent mean gas temperature and an apparent mean heat transfer coefficient for
cylinder nodes have to be found. To this effect a function  z,  is used in the model.
For every node of the cylinder liner, the function is defined such that:
 z,   0 if
1 if
d pist head    z
d pisthead    z
(10)
Figure 5. Schematic to illustrate the notation used in the modeling of the cylinder gas
– liner interaction.
Being z the axial position along the liner measured from the fire deck, d pist head   is
the distance between the fire deck and the top of the piston for crank angle α (as
illustrated in figure 5). With the δ-function, the mean gas temperature and heat
transfer coefficient are defined for each position along the stroke. The mean heat flux
at a distance z from the fire deck is
720
1
1
q z  
qz, d 

720 0
720
 h  z, T    T z d
720
gas
liner
(11)
0
This can be written as:
qz   hz T gas z   Tliner z 
(12)
With the mean heat transfer coefficient and gas temperature at a distance z from the
fire deck:
720
1
h z  
h .  .d
720 0
(13)
720
1
Tgas  h .  .d
720 0
Tgas z  
h z 
(14)
Considering a node of the cylinder liner between a distance of z 1 and z 2 from the fire
deck, the contact area is given by:


A    .B. z1, z2  z1   1   z2 ,  z2  d pis2head  
(15)
The mean film coefficient times the area gives the conductance that has to be put on
the conductance matrix, K gas_ z _ i  Agas_ z ,i  h ( z ) , for each node of the cylinder liner in
contact with the cylinder gases in the model. The apparent gas temperature seen by
the cylinder ring band, in which the node is located, is used as boundary condition,
Tgas (z ) .
The conductance between the valves and the seats Kvalves–head is the product of a contact
time factor, the valve seat area (Aseats) and a contact conductance (Kseat): Kvalves–
2
head=f.Aseats.Kseat. For the contact resistance, Kseat, a value of 3000 W/m K was used [21].
Gas-wall heat transfer.
The film coefficient, hgas, necessary to calculate the conductance between the gas and the
walls, is obtained with an enhanced version of Woschni equation [22]:


VT 
hg  1.2 10  2 D 0.2 p 0.8Tg0.53  (C w1cm  C w 2 cu )  C2  T CA  p  p0 
 pCAVCA 


0.8
(16)
Here, D is the bore; Tg the instantaneous gas temperature calculated with the measured incylinder pressure, p; c m is the mean piston speed; cu is the tangential velocity at the
cylinder wall due to swirl; VT is the displacement volume; Tivc, pivc and Vivc are the gas
temperature, pressure and cylinder volume at intake valve closing (IVC) and p0 is the incylinder pressure under motoring conditions.
In the wall temperature model the heat transfer coefficient between the gas and the
walls is calculated with the previously described formula using the instantaneous gas
temperature, Tgas   , and pressure, p  , from a home made combustion predictive
program. Then the cycle average heat transfer coefficient and gas temperature are
calculated.
Runner – air heat transfer
The heat transfer between the runners and the gas is highly non stationary. Especially
in the exhaust where very high gas velocities are reached during the blow down.
Because the generated turbulence lasts even after valve closing, formulas based on the
instantaneous speed cannot describe adequately the heat transfer in this pulsating flow
and in this work the method proposed by Reyes [23] was used. The velocity is
calculated as a sum of the actual velocity and the previous velocities multiplied with
their respective dissipation coefficients (17).

 c V t  kt 
k
V t  
k 0
(17)

c
k
k 0
The average velocity V t  is calculated with the instantaneous velocity V t  and the
previous average velocity V t  t  :
V t   cV t  t   1  cV t 
(18)
Being c the dissipation constant. With the time averaged speed, the Reynolds and
Nusselt numbers are calculated.
Re 
V D

Nu  1.6Re
(19)
0.4
(20)
The instantaneous speed is obtained from the combustion analysis program. The heat
transfer coefficients and temperatures for the intake and exhaust gases, obtained from
the Nusselt number, are averaged over a cycle in a way analogous to the one used to
obtain the in-cylinder mean film coefficient ( h ) and the apparent gas temperature
( T gas ).
Coolant – wall heat transfer
Along three quarters of the stroke the cylinder liner are refrigerated by water. The
correlation for the corresponding conductance (K lin,i–cool) takes into account the
coolant flow dependent convection. A similar conductance (Khead,i–cool) exists between
the cylinder head nodes in contact with the coolant and the coolant itself. Forced
convection is the dominant regime in the coolant circuit and is described with the
widely used Dittus-Boelter correlation [24].
Nu  0.023 Re 0D.8 Pr 0.4
(21)
In the model the possibility of occurrence of the local boiling effects was neglected. The
decision was taken considering the complexity of the problem resulting in significant
deviations of coefficient values calculated according to the different equations and the
multiplicity of variables needed, not all easy to assess.
Oil – Piston heat transfer.
The piston is cooled in two ways. Part of the heat is led away through the segments to
the liner and finally to the coolant. The bigger part, though, is transferred to the oil. In
the engine under study the oil is sprayed to the entrance of a gallery in the piston
crown from an oil cooling jet.
To find the heat transfer coefficient hoil-pis , based on the boundary layer theory, an
expression of the form Nu gal  Re mgal . Pr n for the convective heat transfer in the piston
gallery is used. Since no tests were done with which the value of exponent n could be
determined, it was decided to consider the factor Prn as a part of the constant. The
expression for the Nusselt number then takes the following form:
Nu gal  C gal Re mgal
(22)
The Nusselt number in the coolant gallery is defined as Nu gal 
number as Re gal 
S p .d gal
 oil
hgal .d gal
k oil
, the Reynolds
. Where dgal is the internal diameter of the oil gallery and koil
and υoil are the conductivity and viscosity of the oil, respectively.
Based on the work of Kajiwara [25], using the piston temperature measurements, the
correlation for the conductance between the oil and the piston was sought in the form:
K pis oil  C pis oil S p 
Exp _ pis oil
(23)
Where Sp is the mean piston speed. The parameters Cpis-oil and Exppis-oil determine the
piston speed dependent conductance between the piston and the oil. The constants are
results of the optimisation routine.
Liner – oil heat transfer.
Oil is continuously splashed against the cylinder wall and, in the piston some channels
coming from the cooling gallery feed the third groove. So the cylinder wall is continuously
wetted with oil. This oil is heated by the cylinder wall and scrapped of during the
downward stroke. For this conductance (Klin-oil), a piston speed dependence was taken into
account just like for the oil – piston heat transfer. During the optimization phase of the
model this speed dependence did not appear to be very significant and only the constant
part was included in the model. An equivalent heat transfer coefficient, hlin–oil, for this
mechanism can be extracted from the following expression:
K lin oil  Aij hlin oil
(24)
Piston – cylinder liner heat transfer
Because measurements were available of both the piston and the liner temperature, an
empirical model could be fitted to the data. It was supposed that the segments have a
conductance Kseg per unit of length. The possible influence of the piston speed was
turned to be not significant. Hence the conductance between a node of the piston
“Pis_i” and a node of the liner “Lin_j” which make contact through a segment is given
by the following formula:
t
D
K Pis _ i  Lin _ j  con K seg Lin _ j
(25)
Tcycle
2
Where, tcon is the contact time between the segment and the liner node, T cycle the
duration of a cycle, α Lin_j the angular width of the liner node and D the bore. The
contact time is calculated from the instantaneous piston position taking into account
the position of the segment and the axial position of the liner node.
Cylinder head – cylinder liner heat transfer
Heat conduction between the cylinder liner and the cylinder head is possible through the
gasket (Klin–head). This conductance did not appear to be significant and was not considered
in the model.
3. THE COMPUTATIONAL PROGRAM.
As was mentioned in the previous paragraph the model developed is a combination of
theoretical and experimental work. Fitting the model to particular engine temperature
measurements, it has been taking care of representing the conductances involved in the
optimization process, as functions of geometrical and operational parameters of the engine,
so that the model can be readily applied to other engines with similar geometry and power
as a generic template. Also a set of scale factors and relationships has been provided in the
program to adjust new engine geometries and materials.
The code to model the thermal behaviour of the engine has been written in C++. Its
structure is summarized in figure 6. The inputs of the program are: a file with the
names of the tests, the wall temperatures of which will be calculated; CALMEC (home
made predictive computer application ) output files with the instantaneous temperature
and pressure in the combustion chamber for every test; a file that contains the measured
mean variables representative of the running condiction, including prescribed coolant
and oil temperatures ; a file that describes the discretization of cylinder liner, cylinder
head and piston and, finally, a file with the parameters of the model, needed to
calculate convective conductances.
Figure 6. Structure of the computational program used for the model [15].
The program can be used either in predictive mode, or in an optimization mode. In the
optimization mode, the parameters of the model affecting convective conductances
(with the capability to be extended to other new parameters of interest) are adjusted in
a way that the error between the calculated and measured temperatures of a known set
of tests is minimal. The program uses the Nelder-Mead simplex algorithm [26] to
optimize the parameters.
In the predictive mode, temperatures and heat fluxes can be calculated for any given
engine, provided its geometrical information and the instantaneous and mean variables
are known.
For all the tests in the file “Tests.txt” the program calculates the temperatures, and the
results are compared with the measurements. For the cylinder liner the predicted
temperature at a thermocouple location is calculated by three-dimensional
interpolation between the surrounding nodes. This interpolation uses the position of
the nodes and the thermocouple. To compare measurements and predictions in the
cylinder head and piston a weighting procedure is performed between the nodal
temperatures of close related nodes.
With the engine used to tune the model up, the values of the optimized parameters are
those referred in table 2.
Table 2. Optimized values of conductance parameters used in the model.
Cte_lin2head
0
h_cool2cyl
0.524482
h_cool2FD
1.218676
h_cool2Exh
0
Cte_pis2oil
Exp_pis2oil
Kpis2lin
h_lin2oil
721.422607
0.687376
3.875552
864.868713
4. RESULTS AND DISCUSSION.
The experimental work comprises two stages. The first stage is intended to provide engine
steady state temperature measurements to run the computational program in the
optimization mode. The outcome of this stage is the attainment of the optimized model to
predict the thermal behaviour of Diesel engines geometrically similar to that used in the
model development process.
In the second stage, another set of tests is used to obtain measurements of the engine
temperatures over elementary transient step changes with the aim of assessing the
predictions of the model for heated engine transient operation. Known the initial and final
points of transient engine operation, the model with the optimized parameters is used to
calculate temperature evolution of the engine temperatures and heat fluxes for a given
transient time. An interpolation procedure in the time domain, allows a comparison of
predicted and experimental transient thermal responses of the engine.
For the first stage, the program is run in the predictive mode and the predicted temperatures
are compared to the measured ones, obtaining the model temperature errors separately for
piston, liner and cylinder head, as well as the global model error. After that, the program is
requested to optimize the initial model parameters in the optimization mode, and the
resulted optimized parameters are re-entered to the model to recalculate the engine
temperatures and obtain the global error, the final errors in the predictions of piston, liner
and fire deck temperatures, the heat fluxes between engine nodes and the engine heat
balance.
For the second stage, the program is run in the predictive transitory mode, after optimizing
the model parameters.
The test matrix with the mean variables used during the optimization process of the thermal
model for the engine under study is presented in table 3. 32 steady state tests were
conducted with variation of the speed and load. The temperatures of the 32 tests are
compared to those obtained experimentally for all measured points.
Table 3. Mean variables of the tests performed and used to tune the model up.
Test Speed Tq_C1 mep C_FlB M_a1 P_In1 P_Ex1 T_In1 T_Ex1
-
rpm
Nm
1
1500
2
3
bar
ºC
ºC
TC_B
ºC
ºC
g/s
mbar
15.25 4.93
27.03
5.26
1089
1228
54.9
381.7
1500
15.21 4.92
26.88
5.27
1090
1230
55
382.1
90 95.89
3500
8.14 2.63
62.04 16.74
1548
1655
55
382.2
91.7 96.25
4
3500
14.42 4.66
61.86 17.06
1564
1625
55
434.8
94.7 95.76
5
2500
6.71 2.17
43.86 10.98
1243
1353
55.2
238.7 107.6 95.78
6
2500
21.67 7.01
44.07 13.19
1499
1703
55
390.8 105.1 95.54
7
2000
9.75 3.15
34.86
1206
1312
55.1
8
mbar
T_oil
l/min
90 95.98
280.6 106.3
95.9
8
2000
35.81 11.6
34.78 11.03
1685
1780
54.9
509.3 104.6 95.27
9
2000
22.63 7.31
34.96
9.83
1491
1644
55
410.2 103.4 95.49
10
3000
9.53 3.08
34.79 15.71
1547
1672
55
267.6 106.5 95.65
11
3000
36.38 11.8
34.75 18.39
1813
2094
55.1
532.8
110 94.64
12
3000
36.33 11.7
34.98 18.41
1814
2108
55
532.2
110
13
3000
21.36
35.13 17.03
1673
1842
55
360.3 106.2 95.36
14
2000
22.32 7.21
35.38
9.74
1471
1612
55.1
412.9
75.8 95.84
15
2000
22.48 7.27
35.66
9.74
1473
1610
55.1
413.8
85.1 95.81
16
2000
22.33 7.22
35.55
9.72
1473
1630
55
417.5
94.9 95.69
17
2000
22.47 7.26
35.44
9.72
1474
1630
55
419.4 105.4 95.61
18
3000
20.13 6.51
56.18 16.48
1525
1171
50.1
688.3
80.3 96.04
19
3000
19.89 6.43
56.01 16.46
1526
1156
50
440.5
89.8 95.96
20
4000
11.42 3.69
73.55 19.45
1611
1341
50.1
491.4
85.1 96.21
21
4000
11.51 3.72
73.68 19.43
1613
1338
50.1
492.5
94.9 96.22
22
4000
11.57 3.74
73.73
19.4
1613
1335
50.1
490.3 104.2
23
1520
7.55 2.44
27.03
3.78
1051
1150
52.1
277.6
64.6 45.55
24
1520
8.04
2.6
27.06
3.74
1079
1178
56.6
311.6
89.7
25
1520
8.26 2.67
26.93
3.75
1088
1177
58.9
306.5
88.3 83.26
26
1520
7.76 2.51
26.96
3.77
1046
1162
52.4
301
89 79.82
27
1520
7.76 2.51
26.96
3.76
1054
1151
52.1
292.5
78.6 62.67
28
1430
16.19 5.23
25.11
4.04
1086
1173
56.4
413.1
90
29
2380
31.81 10.3
41.95 10.04
1368
1427
60.4
579.5
90 64.37
30
2380
42 10.07
1353
1383
60.1
583.7
90.1 87.37
31
2380
30.96
10
41.97 10.05
1373
1418
60
586.1
90
32
2380
30.61 9.89
41.92 10.07
1347
1369
60.1
580.4
90 79.17
6.9
31.6 10.2
94.5
96.1
97
97
97
4.1. Temperature of liner nodes.
Figure 7 illustrates the predicted and measured comparison of temperature distribution in
the liner at various axial locations, at a depth of 3,5 mm, for three representative operation
points: 12 %, 33 %, and 65 % of BMEP (tests Nº 1, 6 and 12, in table 3, respectively). In
general it can be observed that the model predicts well the liner temperatures, with a
temperature gradient descending from the top to the bottom for the refrigerated part of the
liner. For the remaining longitudinal fourth part of the liner nodes, the temperatures
experiment a light increment. Main discrepancies (particularly for the liner nodes placed
between cylinders, figure 7,a), and for the nodes located in the longitudinal center of the
liner) may be due to the adoption of a global spaced averaged heat transfer coefficient for
the coolant liner interaction. Actually, within the coolant passages more than one regime
may exist for any given load condition and will vary locally around the coolant circuit. In
the model for the coolant boundary condition, the variations in coolant and surface
temperatures around the coolant circuit are neglected. This can give rise to variations in the
local rate of heat transfer to the coolant around the circuit directly due to variations in the
surface to coolant temperature difference, and indirectly through the effects on heat transfer
coefficients.
Temperatures along the cylinder liner, intake side, for three
typical operating points
145
Temperature (ºC)
Temperature (ºC)
Temperature along the cylinder liner between cylinders 1 and 2
120
128
120
112
104
96
95
0
0
10
20
30
40
50
60
70
80
90
20
40
60
100
80
100
120
distance (mm)
Distance from fire deck (mm)
C_002_predicted
C_033_predicted
C_002_measured
C_033_measured
C_050-predicted
C_050_measured
C_002_predicted
C_050_predicted
C_033_predicted
C_002_measured
C_050_measured
C_033_measured
a)
b)
Temperature along the cylinder liner, exhaust side, for three
typical operating points
Temperature along the cylinder liner, clutch side
Temperature (ºC)
Temperature (ºC)
130
135
123
111
99
122
114
106
98
0
20
40
60
80
100
0
10
20
Distance from fire deck (mm)
30
40
50
60
70
80
90
100
Distance from the fire deck (mm)
C_002_predicted
C_033_predicted
C_050_predicted
C_002_predicted
C_033_predicted
C_050_predicted
C_002_measured
C_033_measured
C_050_measured
C_002_measured
C_033_measured
C_050_measured
c)
d)
Figure 7. Predicted and measured temperature distributions in the liner at various axial
locations for 12 %, 33 %, and 65 % of BMEP: a) between cylinders side, b) intake side, c)
exhaust side, d) clutch side.
The dependence of liner wall temperature on load is exemplified in figure 8, for two
operation points with the same engine speed of 3000 rpm, and mean effective pressures of
3,08 bar and 11,76 bar, correspondingly (tests 10 and 12, respectively). The predictions
agree with the measured data at a good level. As was previously said main discrepancies
may be attributable to the variation of heat transfer coefficient for the liner coolant
interface, less important at low loads.
Temperatures along the cylinder liner, intake side, medium high
speed load band
164
156
148
140
132
124
116
108
100
140
Temperature (ºC)
Temperature (ºC)
Temperature along the cylinder liner between cylinders 1 and 2,
medium high speed load band
132
124
116
108
100
0
10
20
30
40
50
60
70
80
90
100
0
10
20
30
40
Distance from fire deck (mm)
C_045_predicted
C_048_predicted
C_045_measured
C_048_mesured
C_045_predicted
C_048_predicted
a)
60
70
80
90
100
C_045_measured
C_048_measured
b)
Temperature along the cylinder liner, exhaust side, medium
high speed load band
Temperature along the cylinder liner, exhaust side, medium
high speed load band
132
Temperature (ºC)
134
Temperature (ºC)
50
Distance (mm)
124
114
104
124
116
108
100
0
20
40
60
80
100
0
20
Distance from the fire deck (mm)
C_045_predicted
C_048_predicted
c)
C_045_mesured
40
60
80
100
Distance from the fire deck (mm)
C_048_measured
C_045_predicted
C_048_predicted
d)
C_045_measured
C_048_measured
120
Figure 8. Predicted and measured temperature distributions in the liner at various axial
locations as the load changes at a constant speed of 3000 rpm, a) between cylinders side,
b) intake side, c) exhaust side, d) clutch side.
The sensitivity of the model to the speed changes as compared to the measured values is
represented in figure 9 for two operation points with the same mean effective pressure of
2,6 bar and engine speeds of 1520 and 3500 rpm, correspondingly (tests 3 and 24,
respectively). The match of predicted and measured temperatures is good, more accurate at
low speeds.
Temperature along the cylinder liner, intake side, low load
speed band
130
126
122
118
114
110
106
102
98
114
Temperature (ºC)
Temperature (ºC)
Temperatures along the cylinder liner between cylinders 1 and 2,
low load speed band
110
106
102
98
0
10
20
30
40
50
60
70
80
90
100
0
10
20
Distance from fire deck(mm)
C_011_predicted
M2_26_predicted
C_011_measured
30
40
M2_26_measured
C_011-predicted
M2_26_predicted
a)
60
70
80
90
100
C_011_measured
M2_26_measured
b)
Temperature along the cylinder liner, exhaust side, low load
speed band
Temperature along the cylinder liner, clutch side, low load
speed band
110
Temperature (ºC)
112
Temperrature (ºC)
50
Distance from fire deck (mm)
104
96
106
102
98
0
20
40
60
80
100
120
0
20
Distance from fire deck (mm)
C_011_predicted
M2_26_predicted
C_011_mesured
40
60
80
100
120
Distance from the fire deck (mm)
M2_26_mesured
C_011_predicted
M2_26_predicted
C_011_measured
M2_26_measured
c)
d)
Figure 9. Predicted and measured temperature distributions in the liner at various axial
locations as the speed changes at a constant mep of 2,6 bar, a) between cylinders side, b)
intake side, c) exhaust side, d) clutch side.
Liner temperatures as well as all others increase with speed and load. The gradient is more
significant in the upper part of liner. Higher engine loads translate in an increase of
temperatures but with a higher gradient in the upper portion of the liner; higher engine
speeds more equally distribute wall temperatures along the stroke.
The computed temperatures of the liner in the cross sectional area are in good agreement
with experimental results, as can be inferred from the temperature plot in figure 10, where
temperatures for four orthogonal points in the liner at a distance of 44 mm and a penetration
depth of 3,5 mm, for load cases 1 a12, have been represented. It is observed that major
discrepancies in the predicted temperatures as compared to measured values appear for
liner nodes between cylinder nodes, especially at high loads.
Temperature distribution in the transversal section of the cylinder
liner for low and medium high load operation
Between C1 and C2
150
100
C_002_predicted
Clutch side
50
C_050_predicted
Intake side
C_002_measured
C_050_measured
Exhaust side
Figure 10. Distribution of liner node temperatures in the cross sectional area of the cylinder
1 at a distance of 44 mm from the fire deck, 3,5 mm penetration depth.
4.2. Temperatures for the fire deck nodes.
Through the fire deck the heat flow is transferred from the combustion chamber to the rest
of the nodes of the cylinder head, including intake and exhaust pipes, and coolant.
The comparison of predicted (obtained by interpolation of the nodal results) and measured
temperatures of fire deck nodes of the cylinder head, taken at depths of 3,5 mm and 8,7
mm, for all the experimental test conducted, is presented in figure 11. In general it can be
said that the fire deck temperatures are well rendered, especially for low loads. The average
error in the prediction of the fire deck temperatures is 7,5 ºC, which is low for the
applicability of the model (Procurar traer aquí las conclusions de Jaime sobre sensibilidad
con CALMEC a las predicciones de temperature de pared). The higher errors correspond to
the node represented by the injector hole at the exhaust side, at 8,7 mm (with an average
value of 21,35 ºC), and between intake and exhaust valves (with an average value of 7,02
ºC). The error plot for all the tests conducted under steady state operation points is shown in
figure 12.
Betw._intake_and_exhaust_valves,_distribution_side_at_3.5_mm
Exhaust_valve_seat_of_cyl._1,_exhaust_side_at_3.5_mm
180
160
160
Predicted (ºC)
Predicted (ºC)
140
120
100
140
120
100
80
80
60
60
60
60
80
100
120
Measured (ºC)
140
160
80
100
120
Measured (ºC)
140
160
180
Intake_valve_seat_of_cyl._1_at_3.5_mm
Injector_hole_of_cyl._1,_exhaust_side_at_8.7_mm
160
200
180
Predicted (ºC)
Predicted (ºC)
140
120
100
80
160
140
120
100
80
60
60
60
80
100
120
140
160
60
80
100
Measured (ºC)
Intake_valve_seat_of_cyl._1_at_3.5_mm
140
160
Injector_hole_of_cyl._1,_exhaust_side_at_8.7_mm
160
200
180
Predicted (ºC)
140
Predicted (ºC)
120
Measured (ºC)
120
100
80
160
140
120
100
80
60
60
60
80
100
120
140
160
60
80
100
Measured (ºC)
120
140
160
Measured (ºC)
Figure 11. Predicted and measured temperatures in the cylinder head nodes.
45
20
0
9
M
4_
17
9
4_
14
M
3_
12
M
2_
29
M
83
2_
02
M
71
C
_1
83
52
48
42
89
C
_1
C
_0
C
_0
C
_0
C
_0
C
_0
36
C
_0
27
C
_0
C
_0
C
_0
11
-5
02
Temperature error
(ºC)
Error in the predictions of fire deck temperatures
Points of opeations
Exhaust valve seat
Intake valve seat
Between intake and exhaust vales
Injector hole
Between exhaust valves
Between cyl 1 and 2
Figure 12. Plot of the errors in the prediction of fire deck temperatures for the measuring
points.
The predicted temperatures of cylinder head fire deck nodes, for three representative
operation points: 12 %, 33 %, and 65 % of BMEP (tests Nº 1, 6 and 13 in table 2,
respectively) is presented in figure 13. The higher temperatures correspond to the exhaust
valve. To illustrate the sensitivity of the thermal response of the fire deck nodes load
changes, it is presented in the figure 14 the variation of fire deck node temperatures as the
load is changed from 3,08 to 11,76 bar at a constant speed of 3000 rpm (tests 10 and 12,
respectively). To illustrate the sensitivity of the fire deck temperatures to the speed regime
changes, the behavior of the temperatures for the referred nodes is presented in figure 15,
where the test points correspond to a speed variation from 1520 rpm to 3500 rpm with a
mean effective pressure of 2,6 bar (tests 3 and 24, respectively).
Predicted temperatures of fire deck nodes for three typical
operating conditions
Temperature (ºC)
340
280
220
160
100
VLV_A_L_P
AAI_B
AI_B
CENTRAL_B INYTOR_B
VLV_E_D_P
EI_B
EEI_B
Load cases
C_002_1500_4,93
C_050_3000_11,74
C_033_2500_7,01
Figure 13. Temperatures for the fire deck nodes predicted by the model.
Predicted temperatures of fire deck nodes at medium high
speed under low and hig load
Predicted temperatures of fire deck nodes at low load under high and low
engine speeds
350
Temperature (ºC)
Temperture (ºC)
230
290
230
170
170
110
VLV_A_L_P
110
AAI_B
AI_B
CENTRAL_B
INYTOR_B VLV_E_D_P
EI_B
Fire deck nodes
3000_rpm_3,08_bar
EEI_B
AAI_B
AI_B
CENTRAL_B
INYTOR_B
VLV_E_D_P
EI_B
EEI_B
Fire deck nodes
2,6_bar_1520_rpm
2,6_bar_3500_rpm
3000_rpm_11,76_bar
Figure 14. Temperatures for the fire deck Figure 15. Temperatures for the fire deck nodes
nodes predicted by the model at a constant predicted by the model at a constant mep and two
speed and two different mean effective different engine speeds.
pressure values.
4.3. Temperatures for the piston nodes.
The steady-state predicted and measured temperatures in the piston nodes, where
thermocouples were placed, are compared in the figure 16 for all the experimental tests
performed. For the bowl rim, the temperatures are well predicted, while for the bowl
bottom the temperatures are overpredicted. This overprediction of the bowl bottom
temperatures has an acceptable magnitude though. The behaviour of temperature
predictions for these nodes are zoomed in figure 17 for three working operating points
corresponding to 12 %, 33 %, and 65 % of BMEP.
Piston bowl bottom
Piston bowl rim
300
200
Predicted (ºC)
Measured (ºC)
250
200
150
150
100
100
150
200
100
100
250
150
200
250
Measured (ºC)
Predicted (ºC)
Figure 16. Predicted and measured temperatures in the piston nodes.
Temperature (ºC)
Predicted and measured temperatures of piston nodes for
three typical operating points
280
200
120
Rim
Bottom
Piston nodes
C_002_predicted
C_033_predicted
C_050_predicted
C_002_measured
C_033_measured
C_050_measured
Figure 17. Predicted and measured temperatures in the piston nodes for 12 %, 33 %, and 65
% of BMEP.
The sensitivity of the thermal response of the piston nodes to the load is illustrated in figure
18, as the load is changed from 3,08 to 11,76 bar at a constant speed of 3000 rpm. To
illustrate the sensitivity of the piston nodes to the speed regime changes, the behavior of the
temperatures for the referred nodes is presented in figure 19, where the test points
correspond to a speed variation from 1520 rpm to 3500 rpm with a mean effective pressure
of 2,6 bar.
Predicted and measured temperatures of piston nodes at low
load speed band
Predicted and measured temperatures of piston nodes at
medium high speed under low and high load
300
Temperature (ºC)
Temperature (ºC)
200
160
120
220
140
Rim
Bottom
Rim
Piston nodes
M2_26_predicted
C_011_predicted
M2_26_measured
Bottom
Piston nodes
C_011_measured
C_045_predicted
C_048_predicted
C_045_measured
C_048_measured
Figure 18. Sensitivity of piston node Figure 19. Sensitivity of piston node
temperatures to speed changes at constant load. temperatures to load changes at constant engine
speeds.
Figures 20 and 21 show a good agreement between calculated and measured piston node
temperatures along all the test history, with a mayor degree of overprediction for the piston
bowl bottom.
300
250
200
150
100
50
0
250
200
150
100
C_
00
2
C_
01
1
C_
02
7
C_
03
6
C_
04
2
C_
04
8
C_
05
2
C_
08
3
C_
08
9
C_
17
1
C_
18
3
M
2_
02
M
2_
29
M
3_
12
9
M
4_
14
9
M
4_
17
0
Temperature (ºC)
Predicted and measured temperatures for the piston bowl
bottom for a set of tests
C_
00
2
C_
01
1
C_
02
7
C_
03
6
C_
04
2
C_
04
8
C_
05
2
C_
08
3
C_
08
9
C_
17
1
C_
18
3
M
2_
02
M
2_
29
M
3_
12
9
M
4_
14
9
M
4_
17
0
Temperature (ºC)
Predicted and measured temperatures for the piston bowl rim
for a set of tests
Points of operations
Point of operation
Cyl._1_Bowl_Bottom_Temperature Predict(ºC)
Cyl._1_Bowl_Rim_Temperature Predict(ºC)
Cyl._1_Bowl_Rim_Temperature Measure(ºC)
Cyl._1_Bowl_Bottom_Temperature Measure(ºC)
Figure 20. Test history of predicted and Figure 21. Test history of predicted and
measured temperatures of the piston bowl rim.
measured temperatures of the piston bowl
bottom.
Figure 22 shows the variation of temperature errors for piston bowl rim and piston bowl
bottom for a history of tests. Since the program uses only two experimental piston
temperatures of a total of 41 ones in the entire engine (it was not possible to connect
enough sensors to match all the elements of the meshed model), to collectively calibrate the
global thermal model and give well-conditioned predictions of the engine thermal behavior,
it is not likely to approximate all the measures with the same degree of accuracy. Although
a reevaluation of the weighting factors for the temperatures could improve the predictions,
it is true that a more detailed calibration of the engine model could be made introducing
friction model data from an engine of known dimensions and masses, or obtaining
experimental friction data.
Error in the temperatures of the piston
40
20
10
M
2_
29
M
3_
12
9
M
4_
14
9
M
4_
17
0
_1
83
M
2_
02
C
_1
71
C
_0
89
_0
83
C
C
_0
48
_0
52
C
C
_0
42
C
_0
36
C
_0
27
C
C
-10
_0
11
_0
02
0
C
Error (ºC)
30
-20
Points of operation
Error in the temperature of the piston bowl rim
Error in the temperature of teh piston bowl bottom
Figure 22. Error history in the temperature predictions of the piston bowl rim and piston
bowl bottom nodes.
The behavior of the temperatures predicted by the model for all the nodes in which de
model has been descretized is presented in figure 23. A larger number of temperature
measurements with good distribution uniformity in the piston could improve the predictions
if the objectives of the research were to have a refined piston model.
260
220
180
140
100
C_
00
2
C_
01
1
C_
02
7
C_
03
6
C_
04
2
C_
04
8
C_
05
2
C_
08
3
C_
08
9
C_
17
1
C_
18
3
M
2_
02
M
2_
29
M
3_
12
9
M
4_
14
9
M
4_
17
0
Temperature (ºC)
Predicted temperatures for the piston nodes
Points of operation
piston pik node
Piston rim node
Piston bottom node
Central ring belt
piston skirt
falda
Figure 23. Predicted temperatures of the piston nodes for a test history.
A summary of the errors in the predictions of cylinder head (not only the fire deck), the
piston and liner temperatures as well as the total error of the model is plotted in figure 24.
Mean errors in the evaluation of combustion chamber wall temperatures are summarized in
table 4, being the error in the prediction of piston temperatures the larger one followed by
the error in the prediction of cylinder head temperatures. Liner temperatures give the best
predictions. The global mean error is lower than 10 ºC, and is representative for the
operation points encountered by Diesel engines during the city driving cycles. Results are
very satisfactory. In fact, this error is low enough to allow the model to be used for research
purposes in Diesel engine combustion predictive and diagnosing programs. Also, the
information of the model permits to write the energy balance and the heat fluxes between
the components.
temperature error
(ºC)
Errors in the temperature predictions of combustion chamber
walls for a set of tests
30
20
10
0
1
3
5
7
9
11
13
15
17
19
21
23
25
27
29
31
33
Test history
Error_Liner (ºC)
Error_head (ºC)
Error_Pis (ºC)
Error_total (ºC)
Figure 24. Errors in the temperature predictions of combustion chamber walls.
Table 4. Mean errors in the predicted temperatures of engine metallic parts.
Error_Liner Error_head Error_Pis
Error_total
(ºC)
(ºC)
(ºC)
(ºC)
3.871875 7.3853125
10.84375
7.3675
In figure 25 the surface averaged temperatures of the cylinder liner, piston and fire deck are
presented for an extended set of tests. The model allows calculating the heat fluxes through
the combustion chamber walls. In the following paragraph it will be presented the heat flux
balance for all the nodes used in the model.
Mean temperatures of combustion chamber walls
Temperature (ºC)
320
230
140
50
1
11
21
31
41
51
61
71
Test number
Tm_Piston (ºC)
Tm_head (ºC)
Tm_liner (ºC)
Figure 25. Mean temperatures of the cylinder liner, piston and cylinder head for an
extended set of tests.
4.4. Heat fluxes through node boundaries.
Knowledge about geometry, thermal properties of material, conductances, and node
temperatures is utilized in the model to find the partitioning of the heat rejected to the
combustion chamber walls. So, the model can be easily interfaced with engine combustion
predictive and diagnostics programs. Heat crossing any node interface of the discretized
model can also be found. To give an example of this model feature, based on a particular
operational condition of the engine, mep = 3,93 bar and 1500 rpm (test Nº 1 in table 3),
heat fluxes of importance for the heat energy balance will be detailed here.
Table 5 shows the global heat transfer balance in the main components of the combustion
chamber, for the given engine operation condition (test Nº 1).
Table 5. Heat fluxes through combustion chamber walls (W), derived directly from the
model.
From cylinder gases to liner
From cylinder gases to piston
From cylinder gases to fire deck
From exhaust gases to cylinder head
From cylinder head to intake air
Total heat flux received by the combustion chamber walls
419.102953
668.630687
508.402046
294.044094
15.805118
1874.37466
In the steady state running conditions the total heat flux to the combustion chamber walls
plus the heat flux from exhaust gases to cylinder head are transferred in the end to the
engine coolant. This is currently one of the most important outcomes of the program to be
utilized, since it is a primary input to the design and analysis of engine cooling systems.
In the model presented, the cylinder liner model is decomposed into five longitudinal
sections or cylinder ring bands. The heat to the cylinder liner transferred according to this
geometrical partitioning is presented in table 6 for two running conditions (tests Nº 1 and
13). It can be seen that almost 50 % of the heat through the cylinder liner is transferred by
the upper 10 % of the liner surface in contact with the gases. A more refined partitioning of
the liner along its length can be set in the program.
Table 6. Heat fluxes from cylinder working gas through liner surfaces.
Test
Cylinder belt
I
II
III
IV
V
Total
1500 rpm, 4,93 bar
Heat flux (W)
%
201.952
88.737
61.567
43.684
23.163
419.103
48.187
21.173
14.690
10.423
5.527
100
3000 rpm, 11,74 bar
Heat flux (W) %
667.435
46.709
302.344
21.159
215.432
15.076
156.377
10.944
87.342
6.112
1428.931
100
A coarse description of the paths followed by the heat flow from cylinder gases to the
piston surfaces is as appears in table 7.
Table 7. Heat fluxes through piston surfaces.
Piston surface
Piston central pik
Piston bowl rim
Piston core node
Piston upper crown
Total heat flux through piston surfaces
Heat flux, W
53.324
98.018
93.432
423.858
668.632
%
7.975
14.66
13.974
63.392
100
Heat flowing to the piston from cylinder gases is then transferred, one part to the oil
through piston oil gallery and piston under crown surfaces, and the other part to the
cylinder liner through piston-ring-liner interfaces, as depicted by table 8.
Table 8. Heat fluxes through piston-ring-liner interfaces.
Heat flux from piston to oil
Total Heat flux from piston to cylinder liner
Total heat flux through piston surfaces
Heat flux from upper piston ring belt to cylinder liner
Heat flux from lower piston ring belt to cylinder liner
Total Heat flux from piston to cylinder liner
Head flux (W)
559.783
108.848
668.632
%
83.72
16.28
100
59.485
49.363
54.65
45.35
108.848
100
The cylinder liner receives heat from cylinder gases and piston ring belts. This heat, in turn,
is transferred from the cylinder liner to the coolant and to the oil, as presented in table 9.
Table 9. Heat fluxes from cylinder liner to the oil and coolant.
Heat flux from cylinder gases to the liner
Heat flux from piston to cylinder liner
Total heat flux received by the cylinder liner
Heat flux from cylinder liner to coolant
Heat flux from cylinder liner to oil
Head flux (W)
419.103
108.848
527.951
%
79
21
100
310.2575
217.694
58.77
41.23
In the model developed it is assumed that all the energy transferred by the cylinder and
exhaust gases to the cylinder walls goes to lubricating oil and coolant heating. The
lubricating oil receives heat from cylinder liner and piston in the proportions depicted in
table 10.
Table 10. Heat fluxes to lubricating oil.
Heat flux from cylinder liner to oil
Heat flux from piston to oil
Total Heat flux to oil
Head flux (W)
217.694
559.783
777.477
%
28
72
100
The gas energy balance for the cylinder head is presented in table 11. As can be seen an
important part of the heat flux to the cylinder head comes from the exhaust gases, almost 35
%.
Table 11. Heat transfer between cylinder head and working gases.
Heat flux from cylinder gases to fire deck
Heat flux from exhaust gases to cylinder head
Heat flux to intake air from cylinder head
Total heat flux received by the cylinder head walls
Head flux (W)
508.402046
294.044094
-15.805118
786.641022
%
64.63
34.37
2
100
The detailed description of the heat flows leads us to the determination of the heat
transmitted to the coolant, as presented in the table 12. It is noteworthy that the cylinder
liner participates with less than 20 % in that heat flow. More than 80 % of the heat
transferred to the coolant comes equally from the cylinder head and oil. Almost 16 % of the
heat transferred to the coolant comes from the exhaust gases. 58,56 % of the heat
transferred to coolant comes from the metallic parts, the 41,44 % remaining comes from the
oil.
Table 12. Heat transferred by the engine to the coolant.
Heat flow from cylinder head to coolant
Heat flow from cylinder liner to coolant
Heat flow to coolant coming from combustion chamber walls
Heat flow from oil to coolant
Total heat flow received by coolant per cylinder
Total heat flow to coolant due to combustion in all the engine cylinders
Head flux (W)
786.64
310.26
1096.90
777.476
1874.375
7399.287
%
41.97
16.55
58,56
41.44
100
The detailed heat balance presented can be performed for every point of operation, making
the model suitable to analyse engine cooling systems at any given load operation of a
vehicle in which the engine would be installed.
In figure 26 they are shown the heat fluxes through combustion chamber walls for the
extended set of tests run under stationary conditions. In figure 27 the predicted total heat
flux through combustion chamber walls is compared to the heat rejected by the coolant,
calculated with the in and out coolant temperatures, coolant properties and coolant flow.
The difference between these two curves stands for the result of heat exchanged between
cylinder head and intake and exhaust gases, then transmitted to coolant.
Heat flux through combustion chamber walls
Heat fluxes trough cylinder walls and Heat
evacuated by the coolant
Heat flow (W)
Heat flux (W)
9000
6000
3000
40000
30000
20000
10000
0
1
0
1
11
21
31
41
51
61
31
71
61
Test history
Test number
Q_coolant
q_total (W)
q_pist (W)
q_head (W)
Q_heat_fluxes_walls
q_liner (W)
Figure 26. History of heat fluxes through Figure 27. Comparison between heat fluxes
combustion chamber walls for the test used in through combustion chamber walls and
the optimization of the model
heat rejected to coolant.
Given the availability of the information related to brake effective power and fuel
consumption for the tests performed, the heat losses through combustion chamber walls
were related to the effective power developed by the engine and to the equivalent power
introduced with the fuel. In figures 28 and 29 these useful relationships are presented. A
representative set of tests could be used to predict the thermal map of the engine under
modelling.
Heat flux through cylinder walls to introduced power ratio
Heat flux through cylinder walls to break heat
power ratio
0.35
Q_flux/BHP
2.1
0.25
1.4
0.7
0.15
1
0
1
31
Test history
61
31
61
Test history
Heat flux through cylinder walls to introduced power ratio
Figure 28. Heat losses through combustion Figure 29. Heat losses through combustion
chamber walls related to brake effective chamber walls related to energy introduced
power.
with the fuel power, to be used in
combustion analysis.
Experimental coolant heat flow to introduced power ratio
Power and heat flux
(kW)
Engine energy balance
200
0.56
150
0.42
100
0.28
50
0.14
0
1
31
61
Engine_brake_pow er
Heat floux through cylinder w alls
1
31
61
Test history
Test history
Pow er introduced w ith the fuel
Figure 30. Heat losses through combustion
chamber walls, brake mean effective power
and power introduced with the fuel for a set
of operation points.
Experimental coolant heat flow to introduced power ratio
Figure 31. Heat rejected to the coolant
referred to equivalent power introduced
with the fuel for a set of operation points, to
be used in engine efficiency analysis.
4.5. Transitory results.
After the model has been optimized for the steady state conditions the model can be used to
analyse the engine thermal response predictions of the engine under transient conditions.
Node temperatures and heat flux variations over any transient step determined by any play
of initial and final load operation conditions can be calculated. A time-step length of 1
second was used in these calculations as a compromise between computation efficiency and
prediction accuracy (calculation of the Fourier number for the presumed most risky nodes
was done). The experimental measurements obtained for a set of 31 transient engine
processes between known initial and final conditions were used to assess the model. For
this tests the readings of the 39 thermocouples (for the transient tests difficulties were
encountered with the measurements of piston temperatures) used were registered during a
sufficient period over which the given set of operating conditions were applied on the
system.
In general, although there is still room for improvement, a satisfactory degree of agreement
is found between theoretical predictions and experimental measurements under all
conditions tested.
In figure 32 transition temperatures (at 4500 rpm speed transition from 2 bar mep to 8 bar
mep, and at 1000 rpm speed transition from 3 bar mep to 10 bar mep) for the cylinder liner
measurements at two extreme longitudinal locations are shown. It can be seen that the
model overpredicts the temperature evolution for the upper part, especially at high speeds
and loads. This is caused in part by the error at steady state conditions, and in part also by
the small number of segments taken in the lumped parameter model in the longitudinal
dimension of the liner, which determines the accuracy of temperature resolution. However,
the excursion of the response in a trend of a first order thermal element is acceptable.
Obviously a refinement of the cylinder mesh would approach closer the time constants, but
at the expense of the computational cost. Results for the lower part of the liner, where the
static errors are lower, are satisfactory.
In figure 33 they are also illustrated temperature evolution for all the liner nodes were
experimental information was available. The heat transfer gradient for the first two axial
positions (ie, at 8 mm and 25 mm) is high when compared with the heat transfer gradient at
other positions.
Evolution of temperature of liner nodes along the stroke
Evolution of liner node temperatures for two different operating
points
150
Temperature (ºC)
Temperature (ºC)
150
120
90
0
30
60
90
130
110
120
0
30
60
Time (s)
90
120
Time (s)
4500_2_8_8.8_meas
4500_2_8_8.8_pred
4500_2_8_89.1_meas
4500_2_8_89.1_pred
1000_3_10_8.8_meas
1000_3_10_8.8_pred
1000_3_10_89.1_meas
1000_3_10_89.1_pred
Exh_side_cyl1_8mm_meas
Exh_side_cyl1_8mm_pred
Exh_side_cyl1_25mm_meas
Exh_side_cyl1_25mm_pred
Exh_side_cyl1_81.3mm_meas
Exh_side_cyl1_81.3mm_pred
Exh_side_cyl1_89.1mm_meas
"Exh_side_cyl1_89.1mm_meas
Figure 32. Transient temperatures for a couple Figure 33. Transient temperatures for cylinder
of extreme liner nodes under two transient liner nodes.
processes.
In figure 34, 35 transient temperatures for the fire deck nodes are presented. The thermal
response of the model is somewhat faster as compared to the experimental traces. It is more
favourable the prediction for the exhaust valve seat node. Time constants can be considered
favourable.
Evolution of fire deck node temperature for two different
transient regimes
160
Temperature (ºC)
Temperature (ºC)
Evolution of fire deck node temperature for two different
operating points
130
100
0
30
60
90
120
200
150
100
0
30
Time (s)
60
90
120
Time (s)
4500_2_8_exh_vlv_seat_meas
4500_2_8_exh_vlv_seat_pred
4500_2_8_Betw_exh_vlv_3.5mm_meas
4500_2_8_Betw_exh_vlv_3.5mm_pred
100_3_10_exh_vlv_seat_meas
1000_3_10_exh_vlv_seat_pred
1000_3_10_Betw_exh_vlv_3.5mm_meas
1000_3_10_Betw_exh_vlv_3.5mm_pred
Figure 34. Transient temperatures for the Figure 35. Transient temperatures for the node
exhaust valve seat under two transient between exhaust valves under two engine
processes.
transient processes.
In figure 36, 37 transient temperatures for two fire deck nodes are presented. Plot 37
illustrates two speed transitions at constant load, from 1100 to 2700 rpm, and from 1040 to
4000. The thermal response of the model anticipates experimental traces. As was
mentioned before the accuracy of transient response is limited by the accuracy of steady
state response, which is affected also by the coarseness of the lumped parameters model.
Evolution of predicted and measured temperatures of a exh.
valve seat node during two typical transition regimes
Temperature (ºC)
Temperature (ºC)
Predicted and mesured temperatures for the exhaust valve
seat, two typical transition regimes
160
130
160
140
120
100
0
100
0
30
60
90
25
50
75
100
Time (s)
120
Trans_1100_2700_8,8_exhv_seat_measured
Time (s)
Trans_1100_2700_8,8_exhv_seat_predicted
Trans_1000_3_10_exhv_seat_measured
Trans_1000_3_10_exhv_seat_measured
Trans_1040_4000_8,8_exhv_seat_measured
Trans_2500_4_12_exhv_seat_measured
Trans_2500_4_12_exhv_seat_predicted
Trans_1040_4000_8,8_exhv_seat_predicted
Figure 36. Predicted and measured transient Figure 37. Predicted and measured transient
temperatures for the exhaust valve seat under temperatures for the exhaust valve seat under
two transient processes.
two transient processes.
Because of technical difficulties it was not possible to measure piston temperatures under
transient conditions. The predicted piston response at constant load under a change of speed
is plotted in figure 38. The lower heat capacity of the piston rim allows it to have a quicker
response as compared to piston bowl bottom. In figure 39 transient evolutions of mean
temperatures related to cylinder liner, cylinder head and piston are given for a transition
from operation conditions corresponding to test Nº 32 to those of the operation condition
Nº 1 in table 3. The mean piston temperatures are the more sluggish, though the upper part
of the piston can have a quicker response.
Evolution of the predicted temperatures for piston nodes
during a transition regime at constant load
Evolution of predicted mean temperatures of combustion
chamber walls
240
Temperature
Temperature (ºC)
300
250
200
150
160
80
1
31
61
91
121
151
181
0
30
60
Time (s)
Trans_1040_2700_8,8_bowl_rim
Trans_1040_2700_8,8_bowl_bottom
90
120
Time (ºC)
Tm_Piston
Tm_head
Tm_liner
Figure 38. Predicted transient temperatures Figure 39. Predicted transient temperatures
for the exhaust valve seat under two for the cylinder liner, cylinder head and piston
transient processes.
under two transient processes.
For the already warmed engine, transient total heat flow through combustion chamber walls
establishes very fast, as is illustrated in figure 40 (the combustion process may take from
0,2 to 1,5 seconds to get its steady state). For the transition regimes the time constants for
the engine nodes have an average of 35 – 65 seconds, not considering the time taken for the
combustion process to reach its steady state condition, which is small as compared with this
elapsed time.
In the figure 41 transient heat flux evolution as the engine is subjected to a random driving
cycle arranged with a set of validated transitional processes is plotted. This can serve as an
example of the applicability of the model to simulate the thermal behaviour of the engine
over elementary step changes and stair-step changes in operating conditions, or even to
evaluate the thermal response of the engine over a normalized driving cycle.
Heat flux
Heat flux through combustion chamber walls during a
random driving engine cycle
Heat flux (W)
Heat flux (W)
6000
3500
6000
4000
2000
0
1
1000
0
30
60
90
1001
2001
120
3001
4001
5001
6001
Time (s)
Time (s)
Heat flux through combustion chamber walls
Heat flux
Figure 40. Transient heat flux for a given Figure 41. Transient heat flux evolution as the
change of operational conditions.
engine is subjected to a stair step schedule of
operating conditions.
Finally, to study the potential of developed thermal model for the prediction of engine
thermal performance a second engine was tested with the basic characteristics presented in
table , 85 mm bore, 88 mm stroke, 1,96 MPa maximum break mean effective pressure,
2000 rpm nominal speed. Results of the predicted heat fluxes from exhaust gases to the
cylinder head, heat flux to the oil, heat flux through combustion chamber walls, and heat
losses to the coolant for an arbitrary set of tests is plotted in figure 42. In the same plot the
brake engine power of the tests is drawn also.
Table 13: Second engine main characteristics
Stroke
88 mm
Bore
85 mm
Maximum BMEP
1,96 MPa
Nominal speed
2000 rpm
Engine power and heat losses
Power and heat
losses (W)
80000
60000
40000
20000
0
1
3
5
7
9 11 13 15 17 19 21 23 25 27 29
Test history
q_head_exh (W)
Q_engine_cool_M (W)
Potencia_motor (W)
q_walls_oil (W)
Qflux_wall (W)
Figure 42. Presentation of power and heat balance for the second engine.
The computed mean temperatures of the cylinder liner, fire deck and piston for the second
engine are illustrated in figure 43. For each combustion chamber wall (piston, head, liner),
the mean heat flux over a thermodynamic cycle to the wall area has been also obtained.
Mean temperatures of combustion chamber
surfaces
350
Mean surface
temperature (ºK)
300
250
200
150
100
50
1
3
5
7
9
11 13 15 17 19 21 23 25 27 29
Test history
Tm_Piston (ºC)
Tm_head (ºC)
Tm_liner (ºC)
Figure 43. Mean surface averaged temperatures of combustion chamber walls.
In the progress of our work, the modelling of engine warm-up is under research. Figure 44
shows the temperature variation of the cylinder head, liner, piston, coolant, oil, and external
wall surface temperature of the cylinder head, in the first 1180 seconds engine warm-up
period. The shapes of the curves are encouraging.
Engine temperature during warm-up
Temperature (ºC)
250
200
150
100
50
0
0
200
400
600
800
1000
1200
Time (s)
T_coolant_medio (ºC)
T_oil (ºC)
Tm_Piston (ºC)
Tm_head (ºC)
Tm_liner (ºC)
Tmedia_bloque ºC
Figure 44. Time dependence of predicted mean surface averaged temperatures of
combustion chamber walls, and measured temperatures of coolant and external surface of
the cylinder head.
To gather experimental information for the modelling of engine warm-up, mean variables
and instantaneous values of in-cylinder variables have been recorded during a real warm-up
process. To have the mean variables for every point in the warm-up process, time averaged
values of measurements taken during an actual warming-up process were utilized. It was
assumed that during this transition period, for a given time averaged mep, the instantaneous
in-cylinder pressures are identical for steady and unsteady operations. In fact during the
warm-up, mep is affected by the friction mean effective pressure itself depending on the oil
viscosity. It must be reminded that our model does not accounts for friction as an
independent heat source.
It was assumed that, given the rapidity with which the processes take place inside the
cylinder as compared to the time taken by any operation conditions to become stable, the
cycle-averaged heat transfer coefficient and temperature were still valid for warm-up
transient conditions. An engine can perform a significant number of complete
thermodynamic gas cycles prior to being noticeable affected by transient thermal conditions
resulting from a change in engine operating conditions.
The assumption made above is additionally allowed by the high speed features of the data
acquisition system used to acquire the experimental data, very high as compared to the
times of change of mean variables.
5. CONCLUSIONS.
A lumped parameter thermal model (lumped capacity method), obtained as an extension of
the three nodes concise wall temperature model performed and reported by our research
group [15], has been implemented and validated using experimental data issuing from
thermal steady state and transient conditions. Global measurements of engine variables
from the test bench along with instantaneous values of in-cylinder media properties,
effective valve sections, flows, and local measurements of temperatures in the engine solid
masses, coolant and oil were used during the development process. The updated model
allows a higher degree of discretization and provides local and global heat flow and
temperature field information to support not only energy, but also other relevant issues as
thermal loads required for structural analysis, thermal management studies, and interfacing
to engine cooling systems models. The model uses a geometric template that can be used
for a set of engines with certain degree of structural and geometrical similarity.
To appreciate the predictive capability of the model, there were compared measured and
calculated metallic temperatures for 32 different steady state tests and 31 transient
processes. The heat transferred to the coolant was also calculated as the final end of the
engine heat balance. A second engine was used to validate thermal steady state and
transient predictions. The model gives numerical results closed to the experimental ones on
a wide range of operating conditions. The model can be used as a design tool for thermal
performance optimization and energy management system.
The next phase of the research project is the development of a reduced order thermal
system in which the presented developed model will be coupled to an external to the engine
radiator cooling loop, completing an engine cooling system. This will allow studying the
impact of different cooling strategies on on oil, coolant and metal temperature.
Actual engine speeds, mep and other mean variables, as well as instantaneous in-cylinder
parameters for an engine subject to the acceleration schedule of NEDC have been
experimentally recorded, and used to predict the engine metal temperatures evolution and
heat balance, given the availability of the model. This part of the work shown the
predictive capability of the model to assess the warming-up process of Diesel engines. The
refining of this feature is under work.
Further study and enhancement of the program comprises a more detailed calibration of the
engine model, introducing friction model data from an engine of known dimensions and
masses, and a more accurate prediction of the component thermal transients interfacing the
model to the back of an engine cycle simulation model.
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