INTRODUCTION
Heat transfer through the cylinder side walls is an important process
in determining overall performance, size and cooling capacity of an Internal
Combustion Engine (ICE). It affects the indicated efficiency because it
reduces the cylinder temperature and pressure and thereby decreasing the
work transferred on the piston per cycle. The heat loss (transfer) through
the walls is in the range of 1015% of the total fuel energy supplied
to the engine during one working cycle (Sanli et al., 2008). During
the last decades results from various theoretical and experimental researches
have been presented in the literature on this subject (Rakopoulos and
Mavropoulos, 2008; Mohammadi et al., 2008; Torregrosa, 2006).
Heat transfer in internal combustion engines is extremely complex, since
the relevant phenomena are transient, threedimensional and subject to
rapid oscillations in cylinder gas pressure and temperatures, while the
moving boundaries of the combustion chamber add more to this complexity
(Rakopoulos et al., 2004a). In recent years, the interest for the
heat transfer phenomena in internal combustion engines has been greatly
intensified, because of their major importance, among other aspects, on
successful simulations of thermodynamic cycles and investigations of thermal
loading at critical places in the combustion chamber components (Rakopoulos
et al., 2004b).
Cylinder wall insulation is an interesting design parameter of the engine
cylinder, which has been dealt with in the past mainly as regards heat
transfer, flow and thermal shock calculations. (Rakopoulos et al.,
2004a).
A twodimensional transient Heat Conduction in Components code (HCC)
was successfully set up and extensively used to calculate the temperature
field existing in real engine combustion chambers. In order to obtain
the temperature distribution on the chamber surfaces a method needed to
be developed to calculate the temperature distribution on the chamber
surfaces with the aid of basic heat conduction equations. The Saul`yev
method, an explicit, unconditionally stable finite difference method,
was used in the code. The KIVAII code provided the instantaneous local
heat flux on the combustion chamber surfaces and the HCC code computed
the timeaveraged wall temperature distribution on the surfaces. If material
property data and appropriate coolantside boundary conditions are available,
obtaining satisfactory combustion chamber surface temperature distributions
with this method will be possible (Liu and Reitz, 1997).
Objective of this research is to utilize a multidimensional combustion
model accompanied by an analytical approach to investigate cylinder wall
heat conduction. For this purpose, combustion process is simulated by
the use of FIRE CFD tool to give mean inner wall temperature variation
with crank angle degree to be used as inner wall boundary condition in
Duhamel`s method. Numerical results were validated via experimental data
for OM_355 DI diesel engine for mean cylinder pressure. Diagrams will
be given to show how, the cylinder material, the insulation material and
thickness, Affect the heat flux to the outer walls, the variation of cylinder
temperature with cylinder depth and time in crank angle degree.
MATERIALS AND METHODS
Here, CFD simulation and analytical approach formulation are described:
COMPUTATIONAL FLUID DYNAMICS SIMULATION
Basic equations: The conservation equations are presented for
the following dynamic and thermodynamic properties (FIRE v8.5 Manuals):
• 
Mass → equation of continuity 
• 
Momentum (Newton`s 2nd law) → NavierStokes equations 
• 
Energy (1st law of Thermodynamics) → equation of energy 
• 
Concentration of species equation 

Fig. 1: 
Twodimensional grid of the modeled engine 

Fig. 2: 
Multiblock structure of the grid 
Computational grid generation: Based on the geometry description,
a set of computational meshes covering 360°CA is created. The mesh
generation process is divided into the creation of 2D and 3D mesh. The
2D mesh of the modeled engine is shown in Fig. 1. A
90 degree sector mesh was used in this study considering that the diesel
injector has four nozzle holes. This mesh resolution has been found to
provide adequately independent grid results. The multiblock structure
of the grid, containing spray and injector blocks, is shown in Fig.
2.
Overview of typical boundary conditions: The wall (surface) temperatures
(cylinder liner, cylinder head and piston crown) are based on experimental
experiences and depend on the operating point (load and speed). The boundary
conditions of the cylinder head are specified as fixed wall, the boundary
conditions of the piston bowl as moving wall. In Fig. 3,
overview of the selected boundary conditions is shown.
Symmetry boundary conditions are applied to the radius surface along
the center axis of the segment mesh. This symmetry boundary conditions
might cause problems with calculation results regarding temperature. In
this case adiabatic fixed wall boundary conditions can be specified. In
Fig. 4, details of the boundary conditions is shown.

Fig. 3: 
Boundary conditionsoverview 

Fig. 4: 
Boundary conditionsdetails 
The boundary conditions concerning the additional compensation volume
are applied in this way. Faces at the outer, inner and lower side of the
volume are specified as moving wall adiabatic (heat flux = 0). Figure
5 shows the moving wall adiabatic boundary conditions.
The faces in polar direction are specified as cyclic boundary conditions.
Figure 6 shows selections for cyclic boundary conditions.
Model formulation: The AVL FIREv8.5 CFD tool was implemented to
simulate diesel engine combustion. FIRE solves unsteady compressible turbulent
reacting flows by using finite volume method. Turbulent flow in the combustion
chamber was modeled with k−ε turbulence model. An eddy breakup
combustion model was implemented to simulate the combustion process in
a diesel engine. The reaction mechanism used for the simulation of the
autoignition of the diesel fuel is based upon an extended version of
the well known SHELL model.

Fig. 5: 
Moving wall adiabatic boundary conditions 

Fig. 6: 
Selections for cyclic boundary conditions 
Autoignition model: The SHELL ignition model (Baumgarten, 2006)
was implemented as the autoignition model in this study. The model uses
a simplified reaction mechanism to simulate the autoignition of hydrocarbon
fuels. The mechanism consists of eight generic reactions and five generic
species. The reactions represent four types of elementary reaction steps
that occur during ignition, namely, initiation, propagation, branching
and termination. The five generic species include fuel, oxygen, radicals,
intermediates species and branching agents. These reactions are based
on the degenerate branching characteristics of hydrocarbon fuels. The
premise is that degenerative branching controls the twostage ignition
and cool flame phenomena seen during hydrocarbon autoignition. A chain
propagation cycle is formulated to describe the history of the branching
agent together with one initiation and two termination reactions.
This model has been successfully applied in diesel ignition studies.
It has been found that the ratelimiting step in the kinetic path is the
formation of the intermediate species and the ignition delay predictions
are sensitive to the preexponential factor A_{f4} in the rate
constant of this reaction. Therefore, the above kinetic constant is adjusted
to account for fuel effects.
Combustion model: The EBU model (Brink et al., 2000), has
been developed assuming that in most technical applications the chemical
reaction rates are fast compared to the mixing. Thus, the reaction rate
is determined by the rate of intermixing of fuel and oxygencontaining
eddies, i.e., by dissipation rate of the eddies. For such a case, the
EBU model can be written:
where, Y is the mass fraction and r_{f} the stoichiometric coefficient
for the overall reaction written on mass basis. A and B are experimentally
determined constants of the model, whereas k is the turbulent kinetic
energy and ε its dissipation rate. The product dependence for the
reaction rate is a deviation from the pure fast chemistry assumption,
since the assumption here is that without products the temperature will
be too low for reactions. This model assumes that in premixed turbulent
flames, the reactants (fuel and oxygen) are contained in the same eddies
and are separated from eddies containing hot combustion products. The
chemical reactions usually have time scales that are very short compared
to the characteristics of the turbulent transport processes. Thus, it
can be assumed that the rate of combustion is determined by the rate of
intermixing on a molecular scale of eddies containing reactants and those
containing hot products, in other words by the rate of dissipation of
these eddies. The attractive feature of this model is that it does not
call for predictions of fluctuations of reacting species (FIRE v8.5 Manuals).
Spray and breakup modeling: Currently the most common spray description
is based on the Lagrangian discrete droplet method (Burger et al.,
2002). While the continuous gaseous phase is described by the standard
Eulerian conservation equations, the transport of the dispersed phase
is calculated by tracking the trajectories of a certain number of representative
parcels (particles). A parcel consists of a number of droplets and it
is assumed that all the droplets within one parcel have the same Physical
properties and behave equally when they move, breakup, hit a wall or
evaporate. The coupling between the liquid and the gaseous phases is achieved
by source term exchange for mass, momentum, energy and turbulence. Various
submodels were used to account for the effects of turbulent dispersion
(Barata, 2008), coalescence (Post and Abraham, 2002), evaporation (Baumgarten,
2006), wall interaction (Andreassi et al., 2007) and droplet break
up (Liu et al., 2008).
ANALYTICAL APPROACH FORMULATION
Heat transfer rate from gas to cylinder wall is a harmonic function of
time; therefore a Fourier series analytical solution was implemented.
For simplification it was assumed that there is a uniform temperature
distribution on inner side of cylinder wall. Heat conduction through the
cylinder wall was considered to be one dimensional, this sounds reasonable
because there is a faster variation of the temperature in a direction
normal to the wall surface. In order to calculate the heat transfer rate,
from IVC to EVO, transient equation of heat conduction is solved using
appropriate boundary conditions. Total temperature, T(r, t), which contains
steady and periodic temperature terms, must satisfy one dimensional heat
conduction equation in each time t and for all positions r:
where, α is the thermal diffusivity coefficient. Equation
6 is solved by being separated into steady and transient parts.
Steady heat conduction problem: Because of the greater cylinder
diameter compared with its thickness it can be considered as a slab. In
this model outer wall temperature, T_{c} (is approximately equal
to mean coolant fluid temperature) is known. Thus steady equation of temperature
distribution through a wall with a thickness of l_{w} =
r_{outer} −r_{inner} is:
In Eq. 7, T_{mw} is the mean inner wall temperature
extracted from CFD simulation of the combustion.
Periodic heat conduction problem: Periodic term of the temperature,
T_{p} (r, t), must satisfy the following equation in each time
t and for all positions r:
Equation 8 is solved analytically by using Fourier
technique. The boundary conditions are as follows:
In steady engine operation, mean inner wall temperature is a periodic
function in the calculation domain (from IVC to EVO). So, it can be written
as a Fourier series:
where, T_{m} is the time averaged term, A_{n} and B_{n}
are the Fourier coefficients, n is a harmonic and ω is angular frequency.
The coefficients may be calculated by the following formulas:
Now temperature can be written in exponential form:
Where:
And
Now having the temperature distribution enables us to easily calculate
the heat flux by the use of Fourier law:
ENGINE SPECIFICATIONS, OPERATING CONDITIONS AND INVESTIGATED CASES
The OM_355 Mercedes Benz diesel engine is used in this simulation. The
specifications of mentioned engine are shown in Table 1.
Table 1: 
OM355 engine specifications and operating conditions 

Table 2: 
Different cases defined to study 

Table 3: 
Physical properties of the different materials used (Heywood, 1988) 

Equation 17 shows how the equivalence ratio in Table
1 is calculated. Table 2 shows the different cases
defined to study. Table 3 shows the physical properties
of the different materials (Heywood, 1988).
RESULTS AND DISCUSSION
Here, the results of the diesel combustion simulation are discussed first and
later the analytical results of the wall heat conduction are talked over. In
the analytical part effects of the cylinder wall material, insulation material
and thickness are argued.
Results of the diesel combustion simulation: Figure
7 shows the comparison of mean cylinder pressure for present calculation
and experimental data (Pirouzpanah et al., 2003). As it can be
seen, the agreement between two results is very good.
Figure 8 shows the variations of mean cylinder temperature
with crank angle.
Figure 9 exhibits diesel combustion behavior containing
premixed and diffusion stages of combustion. Comparing this diagram with
temperature and pressure diagrams shows high rates of temperature and
pressure rise during the premixed combustion period.

Fig. 7: 
Comparison of cylinder pressure for Model and experiment (Pirouzpanah
et al., 2003) 

Fig. 8: 
Variations of mean cylinder temperature with crank angle 

Fig. 9: 
Heat release rate diagram 
Figure 10 shows the accumulated heat released in diesel
combustion. In Fig. 11 and 12 mean
inner wall temperature and mean temperature difference between cylinder
gas and inner wall surface are demonstrated.

Fig. 10: 
Accumulated heat release 

Fig. 11: 
Mean inner wall temperature 

Fig. 12: 
Mean temperature difference between cylinder gas and inner wall
surface 
The mean inner wall temperature
was used as boundary condition for analytical procedure. By comparing Fig. 12 and 13, which shows the
variation of wall heat flux, it can be drawn that (T_{gas}−T_{wall}),
has its minimum values and this is accompanied by the lowest levels of
heat flux, in crank angles from about 310 to 330.
Figure 14 shows the near wall temperature based heat
transfer coefficient; comparing this graph to Fig. 13
shows that in crank angles between about 360365, higher heat transfer
coefficients comes along with greater values of heat rejection out of
the in cylinder control volume.
Results of the analytical solution: In the following diagrams
results obtained from analytical solution of heat conduction in cylinder
wall are discussed. x = r−r_{inner} is the penetration depth
in the cylinder wall.
Effect of cylinder wall material on temperature distribution (cases
1 and 2): Figure 1519 show the variations of wall
temperature vs crank angle and position for cases 1 and 2.

Fig. 15: 
Variation of wall temperature vs crank angle for different cylinder
wall depth in case 1 

Fig. 16: 
Variation of wall temperature vs cylinder wall depth for different
crank angles in case 1 
It can be seen
that in the diagrams of temperature vs. crank angle, increase in depth
leads to a fall off and delay in temperature peak and that is because
of the reduction of temperature oscillation with depth. In the diagrams
of temperature vs. depth, increase in depth is along with damping of temperature
oscillations after and it seems that temperature graphs come together
after a distance. Because of the lower thermal diffusivity, this distance
is smaller for case 1 in comparison with case 2. Another important behavior
to be mentioned is that, temperature decreases with depth up to TDC, but
after this time it increases first and then decreases with depth. In another
words before TDC position, maximum temperature occurs on inner wall surface
but after that it is somewhere inside the wall.

Fig. 17: 
Variation of wall temperature vs crank angle for different cylinder
wall depth in case 2 

Fig. 18: 
Variation of wall temperature vs cylinder wall depth for different
crank angles in case 2 
Effect of insulation material and thickness on temperature distribution
(cases 36): Here, effect of insulation material and thickness on
temperature distribution is investigated. Figure 1826
show the variations of wall temperature vs crank angle and position for
cases 36. Comparing Fig. 19 and 21
shows that increasing the insulation thickness results in lower outer
wall temperature. There is a breakage in temperature graph, at the boundary
face between the insulation and the cylinder wall in Fig.
20 and 22. That is because of the sudden increase
of the thermal diffusivity which leads to a decrease in the temperature
gradient.

Fig. 19: 
Variation of wall temperature vs crank angle for different cylinder
wall depth in case 3 

Fig. 20: 
Variation of wall temperature vs cylinder wall depth for different
crank angles in case 3 
By comparing Fig. 19 and 23,
it can be seen that for the same thickness of the insulations case 3 exhibits
earlier occurrence of the temperature peak and also a greater value of
it compared to case 5. It says that in the case of Ins1 more heat can
penetrate faster into the wall.
Figure 2326 show the variations of wall temperature
vs crank angle and position for cases 5 and 6.
Figure 27 shows the outer wall heat flux for different
cases. Case 2 lets more heat flux out of the wall and its related to its
greater thermal diffusivity. In cases 3 and 4 and also in 5 and 6, increasing
the insulation thickness lead to lower outer wall heat flux. Since, The
ins2 has a low thermal diffusivity, it provides the least amount of heat
rejection at the outer wall, even with lower thickness.

Fig. 21: 
Variation of wall temperature vs crank angle for different cylinder
wall depth in cases 4 

Fig. 22: 
Variation of wall temperature vs cylinder wall depth for different
crank angles in case 4 

Fig. 23: 
Variation of wall temperature vs crank angle for different cylinder
wall depth in case 5 

Fig. 24: 
Variation of wall temperature vs cylinder wall depth for different
crank angles in case 5 

Fig. 25: 
Variation of wall temperature vs crank angle for different cylinder
wall depth in case 6 

Fig. 26: 
Variation of wall temperature vs cylinder wall depth for different
crank angles in case 6 

Fig. 27: 
Variation of outer wall heat flux for different cases 
By decreasing
the heat transfer from combustion chamber to the outer wall, more thermal
efficiency can be achieved.
Main results: From this study, on the above mentioned cases on
diesel engine modeling, the following conclusions may be drawn:
• 
The research demonstrated that the combination of multidimensional
and analytical methods is useful for diesel engine wall heat transfer
modeling. 
• 
In the diagrams of temperature vs. crank angle, increase in depth
led to a fall off and delay in temperature peak. 
• 
In the diagrams of temperature vs. depth, increase in depth came
along with damping of temperature oscillations and the temperature
graphs came together after a distance. This distance was smaller for
case 1 in comparison with case 2. 
• 
Before TDC position, maximum temperature occurred on inner wall
surface but after that it was somewhere inside the wall. 
• 
Increasing the insulation thickness resulted in lower outer wall
temperature and lower outer wall heat flux. 
CONCLUSIONS
In the present study, the multidiensional combustion modeling was carried
out for diesel engine. The numerical combustion simulations were done
by the use of FIRE CFD tool. Also an analytical simulation was performed
in order to investigate cylinder wall heat conduction. Analytical simulation
was executed for six different cases of cylinder material and insulations.
Numerical results were validated via experimental data for OM_355 DI diesel
engine for mean cylinder pressure. There have been good agreements between
experiments and the CFD calculations. For the purpose of achieving a low
heat rejection condition from the above engine combustion chamber the
effect of cylinder wall material, insulation material and thickness were
studied. Alluminium chamber let more heat to the outer wall. But using
cast iron as the cylinder material, along with the insulation coating
on the inner wall reduced the outer wall temperature and heat flux noticeably.
NOMENCLATURE
U 
= 
Velocity (m sec^{1}) 
P 
= 
Pressure (pa) 
H 
= 
Enthalpy (J) 
T 
= 
Temperature (K) 
C 
= 
Species concentration (mol m^{3}) 
k 
= 
Turbulent kinetic energy (m^{2} sec^{2}) 
m 
= 
Mass flow rate (kg sec^{1}) 
Y 
= 
Mass fraction 
c 
= 
Specific heat (J kg^{1} K) 
r_{f} 
= 
Stoichiometric coefficient 
l_{w} 
= 
all thickness (m) 
r 
= 
Cylinder wall radius (m) 
ρ_{r} 
= 
Combustion reaction rate (kmol m^{2} sec^{1}) 
A_{n} and B_{n} 
= 
Fourier coefficients 
q_{w} 
= 
Heat flux (W m^{2}) 
Greek symbols
ρ 
= 
Density (kg m^{3}) 
μ 
= 
Viscosity (kg m.sec^{1}) 
λ 
= 
Thermal conductivity (W m.K^{1}) 
φ 
= 
Equivalence ratio 
ω 
= 
Combustion reaction rate (kmol m^{2}.sec) 
ε 
= 
Turbulent dissipation rate (m^{2 }sec^{3}) 
ω 
= 
Angular frequency (rad sec^{1}) 
α 
= 
Thermal diffusivity (m^{2} sec^{1}) 
Subscripts
st 
= 
Stoichiometric 
act 
= 
Actual 
w 
= 
Wall 
c 
= 
Coolant 
p 
= 
Periodic 