Article citation information:
Gustof, P., Hornik, A., Czech, P., Jędrusik, D. The influence of engine
speed on the thermal stresses of the piston. Scientific Journal of Silesian University of Technology. Series
Transport. 2016, 93, 23-29. ISSN: 0209-3324. DOI: https://doi.org/10.20858/sjsutst.2016.93.3.
Piotr
GUSTOF[1], Aleksander HORNIK[2], Piotr CZECH[3], Damian JĘDRUSIK4
THE
INFLUENCE OF ENGINE SPEED ON THERMAL STRESSES OF THE PISTON
Summary. In
the paper, numeric calculations relating to the influence of engine speed on
thermal stresses of the piston in a turbocharged diesel engine in the initial
phase of its work were carried out. The calculations were based on experimental
studies and the data resulting from them. They were made using a geometrical
model of the piston in a turbocharged diesel engine with a capacity of 2,300 cm3,
with a direct fuel injection to the combustion chamber and a power rating
of 85 kW. Modelling of the thermal stresses of the piston was carried out for
the engine speed n=2,000 min-1 and n=4,250 min-1.
Keywords: diesel
engine, thermal stresses, piston
1. INTRODUCTION
Along with an increase in the
mechanical loads, increasing engine power is also accompanied by an increase in
thermal loads. These loads have a significant influence on features of the
engine, such as the exhaust blowing through to the crankcase, the engine oil
wear or the level of pollutants emitted by the engine into the atmosphere. In
particular, a piston experiencing thermal stresses, which are variable
over time, is exposed to these effects. Already at the stage of preliminary
design work, knowledge of the thermal loads of the piston will be required.
Such information can be obtained by suitable modelling of the temperature
distribution in the studied cross sections of the piston’s characteristic
surfaces. Design works and model tests are very expensive and prolonged.
However, the application of mathematical models and suitable computer
techniques allows for determining the temperature distribution for different
materials, sizes and shapes of the piston [1, 8]. Subsequent analysis of this
information helps to formulate initial design assumptions, as well as modernize
existing solutions for operating the engine at various speeds and loads. Very
good results in studies on thermal stresses of the piston are provided by the
application of the finite element method. However, in order to carry out
any numerical calculations, some assumptions and use of empirical methods of
data gathering for each of the analysed operation conditions of the engine are
needed.
2. ANALYSES OF THE
INFLUENCE OF SELECTED PARAMETERS ON THE THERMAL LOADS OF THE PISTON
The conditions of the engine
operation include a change in the effective pressure. Assuming that mechanical
efficiency is constant, an increase in the average effective pressure is
equivalent to a higher heat emission, which leads to an increase in the piston
temperature. The influence of the increase in the average effective pressure on
unit heat flux for the parameter characterizing the heat load of the
cylinder results from the following dependence:
(1)
where:
b = coefficient of the amount
of strokes (for four strokes, b=2)
η =
fill coefficient
cm = average
velocity of the piston [m/s]
D = diameter of the cylinder
[dm]
pd = pressure at
the inlet valve [MPa]
Td = temperature at
the inlet valve [K]
pe = average
effective pressure [MPa]
ge = actual fuel consumption [g/kWh]
T0 = ambient
temperature (T0=293 K)
The increase in the average
effective pressure of a diesel engine is achieved by injection of a higher dose
of fuel per working cycle into a cylinder. Thus, a higher amount of heat is
transferred to the piston while reducing the excess air ratio. The lower the
excess air ratio λ, the larger the relative amount of heat that may be
released from the fuel in the cylinder. The temperature changes are analogous
to the changes in engine power. Both the mixture enrichment and impoverishment
cause a drop in the temperature of the piston. With a too-rich mixture, a large
part of the fuel is not burned. A lean mixture burns slowly, reducing the combustion
temperature, despite the fact that, as a result of chronic combustion, the temperature
of the exhaust gas increases. In a diesel engine, an increase in the engine
load leads to a decrease in the excess air ratio λ, resulting in the
supply of more fuel. It leads to an increase in the amount of heat released in
the engine’s combustion chamber and in the temperature of the elements
surrounding it.
Another parameter affecting the
thermal load on the piston is the engine speed. The influence of this
parameter is quite complicated. On the one hand, an increase in the engine
speed is equivalent to an increase in the frequency of combustion in the
cylinder, increasing the amount of heat in the combustion chamber. On the other
hand, it affects the change in the engine-filling efficiency and thus the
course of the combustion process itself. In a diesel engine, the amount of fuel
being provided into the cylinder does not depend on the engine-filling
efficiency with air, given that, for all rotational speeds, the engine sucks in
a different, albeit maximum, value of the air mass. The amount of the injected
fuel depends on the curve of the dosing characteristic of the injection pump
and on the excess air ratio, which in turn depends on both the amount of intake
air and injected fuel. Figure 5 shows the course of the calculated maximum
values of the piston head surface temperature during a 60-second operation
of a turbocharged diesel engine, calculated by counting from the engine
start its two rotational speeds n=2,000 min-1 and n=4,250 min-1.
Fig. 1. The course of
maximum temperature on the surface of the piston head for two engine speeds
Based on the calculations, it was
found that an almost twofold increase in the rotational speed of a turbocharged
diesel engine for the same load causes lower thermal loads of the piston
head [6]. This is due to a higher speed of heat exchange between the piston and
its environment, in comparison with the amount of heat generated in the
combustion chamber of the engine.
3. MODELLING OF THERMAL STRESSES OF AN ENGINE
PISTON
After starting the engine, the
piston heats up until it reaches a state of equilibrium, which results from the
balance between the heat taken from hot gases in the combustion chamber and
transformed into useful work, and the heat transferred to the environment by,
among others, the coolant and the combustion gases. Determination of thermal
stresses of the piston by means of modelling requires the assumption of
equations and mathematical expressions for the calculations, describing the
process of heat exchange in such a way that the model is able to reflect the
actual processes occurring on the characteristic surfaces. This model was
created for the piston on the basis of the differential equation of the heat
flow in solids.
(2)
where:
a = coefficient of temperature compensation,
cp = specific heat capacity at
constant pressure [J/kgK],
ρ = density [kg/m3],
T = temperature [K],
qv = volumetric efficiency of the
internal heat source [W/m3],
λ = thermal conductivity [W/mK].
The numerical calculations of the
stresses were performed by means of the COSMOS/M program based on the knowledge
of the temperature distribution for assumed operating conditions of the studied
engine. In the program, an actual three-dimensional discrete geometric model of
the piston was created based on the real component. In the model, 16
characteristic surfaces of the piston were distinguished, for which the
temperature distributions and specific values of type III boundary conditions
(Fourier conditions) were determined. These conditions determine the
temperature of the medium surrounding the piston and the heat transfer
coefficients of the characteristic surfaces. These surfaces are shown in Figure
7 [4].
Fig. 2. Characteristic surfaces of the piston
For individual piston surfaces, the
conditions of heat exchange equivalent to those in the combustion chamber
for each cycle of the engine were assumed in the calculations. Based on the
recorded indicator diagrams and the calculated total heat transfer coefficient,
the temperature of the working medium surrounding the combustion chamber
and the values of the heat transfer coefficient for the engine speed of n=2,000
min-1 and speed of n=4,250 min-1 were determined [2-5]. Figures 3, 4, 5
and 6 show the exemplary values of thermal stresses of the piston during a
non-stationary heat flow, corresponding to 10 and 20 seconds of engine
operation measured from its start-up.
Fig.
3. Thermal stresses of the piston after 10 seconds for n=2,000 min-1,
l=1.66
Fig.
4. Thermal stresses of the piston after 10 seconds for n=4,250 min-1,
l=1.69
Fig.
5. Thermal stresses of the piston after 20 seconds for n=2,000 min-1, l=1.66
Fig.
6. Thermal stresses of the piston after 20 seconds for n=4,250 min-1,
l=1.69
4. CONCLUSION
Based on the preliminary results of
the calculations, it can be concluded that maximum values of thermal stresses
of the piston are found mainly in the ring portion and on the surface of the
piston head. On the other hand, the lowest values are found in the guide part.
The obtained maximum values of thermal stresses for the engine speed of
n=2,000 min-1, where λ=1.66, are bigger than thermal stresses for the
engine speed of n=4,250 min-1, where λ=1.69. According to the authors, the
thermal stresses represent an important factor, together with mechanical
stresses, in the design and subsequent operation of the piston for a specified
model and type of engine. However, the calculations should be verified
experimentally in order to obtain the results of numerical calculations, which
ought to correspond with real thermal stresses in the engine during the
warming-up stage in the future [7].
References
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Received
26.07.2016; accepted in revised form 01.10.2016
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