modelling and simulation of the piston combustion engine cooling

Rafał Krakowski
Gdynia Maritime University
MODELLING AND SIMULATION OF THE PISTON COMBUSTION
ENGINE COOLING SYSTEM
In the article, the concepts of the model and purposes of modelling were presented. Various aspects of
graphical modelling was discussed, with particular attention to the bond graph. In the main part of
the paper, was presented model’s description of a piston internal combustion engine cooling system,
in the form of a bond graph. It was shown, that modelling using bond graph requires the presentation
of the system in the form of a graph, routing state equations describing the model of, then their
solution. On the other hand, Lab AMESim simulation software for modelling and analysis of
multidisciplinary mechatronic systems, which, after entering the relevant data, allows direct
simulation. Next a simulation model using block diagrams in the software AMESim was developed.
In the next section, simulations were conducted implementing the software, which enable the
appointment of the courses characteristics of temperature, pressure and coolant pump capacity at
selected points of the system.
Keywords: modelling, simulation, combustion engines, cooling system.
INTRODUCTION
Model of the system presents really existing or imaginary picture that reflects
some actual or hypothetical properties of the test system, its construction, and is
similar to it, in terms of some structural features.
The primary purpose of modelling is to simplify the complex reality, allowing
for subjecting it to a research process. Using modelling, you can reduce or enlarge
the research object to any size, analyze the processes difficult to grasp because of
too fast or too slow pace of their progress or explore one particular aspect of the
problem, ignoring other, less important. The range of phenomena under
consideration depends on the available knowledge and the research model [7].
Currently, in the age of computers and their increasing computing capabilities,
modelling allows to solve many engineering problems early in the design phase.
R. Krakowski, Modelling and simulation of the piston combustion engine cooling system
111
1. MODELLING THE COOLING USING OF THE BOND GRAPH
One way of modelling is the graphic modelling where the model reflects the
dynamic structure of the object and can be easily modified (Fig. 1). Graphical
modelling method include the bond graph, which is a way of modelling physical
systems with energy flow, characterized by a complex structure [3].
Z
U
X
= f [X, U (t )]
X
1
Y = f 2 [ X, U(t )]
X
Y
P
Fig. 1. Model of cause-and-effect described by equations of state in the graphical model:
U – excitations vector (inputs), X – states vector, Y – output vector, Z – noise vector,
P – set vector and construction parameters [3]
Modelling with use of bond graph is applicable in many fields of science and
was also used in the modelling of the piston internal combustion engine cooling
system [5].
The cooling system is a part of the energy system, which is a vehicle driven by
an internal combustion engine. The construction of model of the system requires
pairing it with other elements of the system, mainly to the processing system of the
fuel energy converted into mechanical energy and in the case of the new generation
cooling system with electric power system circuit [5].
Modelling procedure by BG enables you to develop the base model, setting
out the basic energy relationship. The developed model of the cooling system
consists of two related energy subsystems, namely:
• hydraulic system, which introduces the relationship energy combustion engine
(SS) with the electrical system (SE) and the hydraulic system (PCH, ZS, OH),
• heat exchange system.
The equations of state may be generated by software, based on the model
graphic, comprised of two matrix equations: the first-order differential equations
and algebraic equations. The general form of these equations is presented in [4] as
follows:
= f [ X, U(t )],
X
1
Y = f 2 [ X, U(t )],
where:
X – state variables vector of the N elements,
U – excitations vector (inputs) of the M elements,
Y – output vector of the K elements.
(1)
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The linear form of equation (1) gives the relationship:
= A X + B U,
X
Y = C X + D U.
(2)
The elements of the state variables vector X are the average temperatures
assigned to individual elements of the system. The source of energy in this model
(Fig. 2) is part of the flow of energy generated in the working chamber of the
engine (KS) and passed through the walls of the chamber to the coolant:
E KS = TKS ⋅ SKS .
(3)
Energy source in the convention bond graph can be treated in different ways.
In any case, the source energy parameters will depend on the engine control
parameter US [5].
Model bond graph (BG) allows to generate equations of state, which means
creation of a mathematical model of cause and effect. Graphic model consisting of
a single bond graph is created to facilitate the formulation, modifying and verifying
a mathematical model in the form of state equations [2].
Fig. 2. Detailed BG model of the cooling system with regard to modelling some
coolant flows [5]: SS – combustion engine, UP – auxiliary device, UPN – lay-out of drive
moving, TRG – drive gear of t electric generator, GE – alternator, OEE – receivers
of electrical energy to the exclusion pumps of fluidcooling, W – fan, AECH – electrochemical
battery, USCH – control set of cooling system, OH – hydraulic drags of cooling system,
ZS – valve of cooling fluid flow control, PCH – cooling fluid pump
R. Krakowski, Modelling and simulation of the piston combustion engine cooling system
113
The model itself reflects in a clear graphical form, the dynamic structure
of the object and can be easily modified, but does not allow the direct conduction
of simulation experiments.
2. MODELLING OF COOLING SYSTEM IN THE SOFTWARE AMESIM
Simulation testing of the object can be carried out by means of physical
models, built from scratch and developed on the basis of mathematical models in
the form of algebraic equations and differential and selection methods for
numerical solving them. You can either use the library subroutine existing
computing systems, allowing for simplifying the creation of a mathematical model
of the object. In recent years, many computational systems were developed which
allow for the creation of simulation models tested objects. One of these systems is
the AMESim simulation software developed for modelling and analysis of
multidisciplinary mechatronic systems.
AMESim software allows you to solve many engineering problems early in
the design phase. Elements of the system are described by analytical models
representing the behavior of the system components: hydraulic, pneumatic,
electrical or mechanical. It is based on bond graph theory, where causality is
enforced by combining the outputs of one sub-model to the input of another submodel (and vice versa) [1].
2.1. The test stand to research the piston combustion
engine cooling system
Model test stand was developed on the basis of the cooling system with diesel
engine production 4CT90 SW "ANDORIA" SA. The test stand provides conditions
similar to the conditions of operation of the engine cooling. This applies both to the
intensity of heat generation inside the engine cylinders, the temperature distribution
along the axis of the cylinder, as well as variable-speed water pump. The test stand
was made using the following assemblies of engine: the cylinder block with
heaters, head, water pump - driven by an independent electric motor and a radiator
with fans. To drive the water pump was used an electric motor controlled
by inverter with variable speed in the range 0–1850 rev/min. Belt transmission
ratio was chosen so that the rotational speed of the water pump reached a speed
of 4500 rev/min, which roughly corresponds to the rated motor speed. The scheme
of the test stand is shown in Fig. 3.
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Fig. 3. Scheme of the cooling system: 1 – engine block with the head, 2 – cooler in the
horizontal position, 3–5 – solenoid valves, 6–7 – electronic manometers, 8 – shut-off valve,
9 – manometer indication, 10 – inverter, 11 – display and programmer inverter,
12 – electric motor, 13 – water pump, 14 – gear unit 15 – flowmeter, 16 – fan power
switches, 17 – a set of switches, 18 – switches, small and large circulation,
19 – the main switch
The basic component of the test bench and the source of heat being transferred
to the cooling system was the cylinder block with the engine head 4CT90. In each
of the four cylinders the three cylindrical heaters of various electrical power were
placed, which adhered closely to the walls of the engine cylinders. Power heaters
were chosen based on previously
made measurements of the temperature distribution along the cylinder test
engine and temperature distribution in other engines. Roughly equivalent to a heat
flux discharged by the cooling system, a total of approximately 20 kW (Fig. 4):
• upper heater – 2.5 kW,
• central heater – 1.5 kW,
• bottom heater – 1.0 kW.
Fig. 4. Arrangement of heaters
inside the cylinders of the engine [8]
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115
2.2. The model test stand for testing cooling systems
Scheme of the test bench with the cooling system, presented by using block
diagrams in the software AMESim is shown in Fig. 5. Each block in the form
of a picture contains a mathematical representation of the physical characteristics
of a particular element of the test system.
Fig. 5. Scheme of the cooling system in the AMESim software
To perform the calculation of the operating parameters of the cooling circuit,
such as temperature and pressure of the liquid, the expected flow of the pump,
the operation of solenoid valves, you need to enter data into the program, including
the material properties of the liquid and the motor, the parameters of the
environment, the volume of liquid in small and large circulation, weight motor, etc.
2.3. Heat exchange model in the AMESim software
CSRA20 block (Fig. 6) shows the radiator. This block takes into account the
calculation of hydraulic, pneumatic and thermal. Heat exchange between the
coolant and the air is calculated on the basis of the data entered into the program,
which is a function of the volume and flow of the cooling fluid and the velocity
of air flow through the radiator. Is also calculated pressure drop in the radiator.
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The heat exchange between the cooling fluid and the air flowing through the
condenser is a function of the coolant volume and velocity of air flow through the
cooler.
Fig. 6. Block presenting cooler with selected external variables
The experimental data is determined by the experimentally measured
temperature difference:
dTexp = Tcinexp – Tairinexp
(4)
where:
Tcinexp – measured temperature of the coolant at the inlet of the radiator,
Tairinexp – measured temperature of the air at the inlet of the radiator.
Heat transfer is calculated as follows:
Qreal = Qexp ×
(Tcinreal − Tairinreal )
dTexp × seff
(5)
where:
Qreal – the actual intensity of the heat flow,
Qexp – experimental intensity of heat flow,
Tcinreal – the actual temperature of the coolant at the inlet to the cooler,
Tairinreal – the actual temperature of the inlet air to the cooler,
– efficiency of the heat exchanger.
seff
TCV4 block (Fig. 7) is a general submodel of convection between the fluid
and the wall. The wall temperature and the liquid is [°C], and heat flow [W].
Convection is defined by a fluid transfer area, the convective heat transfer
coefficient of liquid/liquid and the temperature of the wall.
Convection heat transfer coefficient is calculated based on the number of
Nusselt (calculated from the number of Grashof (Gr) and Prandtl number (Pr)).
In the general case, the expression Nusselt number takes the form:
Nu = C × (Gr , Pr ) n
(6)
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117
where n = 0.25 for the laminar convection and n = 0.33 for the turbulent
convection.
Fig. 7. Block showing convection between the fluid and the wall
with the selected external variables
Convective heat transfer coefficient hconv is then calculated based on Nusselt
number as follows:
hconv = Nu × λ
cdim
(7)
Finally, the expression for the convective heat transfer takes the form:
dh1 = hconv × cearea × (T2 – T1)
(8)
2.4. Simulation results
Using the simulation program, simulations for different values of overpressure
in the system were performed, the article presents the results for the overpressure
of 0.2 MPa. Simulations were performed for variable filling the cooling system
coolant, which was water without any additives: 10.5 dm3 and 9 dm3, which
represents approximately 95% and 80% in the liquid filling system, where the total
system volume is about 11 dm3. Because in the cooling system the expansion tank
was not installed, the remaining volume of 15% and 20% was the air. The task of
this air was the depreciation of the pressure increase caused by the change in
volume of water and its evaporation. As a result of simulation calculations the
following characteristics were determined: the liquid temperature courses before
and after the cooler and the outlet of the engine, the liquid overpressure courses in
a small and a large circulation flow and the measurement of the coolant pump, and
the results are shown in Fig. 6.
In the simulations carried out at a overpressure of 0.2 MPa and 95% of the
coolant filling for about 27 minutes mild increase of pressure occurred as a result
of the system warm-up. After this time the mean pressure was maintained about
of 0.2 MPa (absolute pressure of 0.3 MPa) with changes in the range of
0.19–0.21 MPa.
Course of overpressure was characterized by a uniformity, but with the high
frequency changes in the intensity of cooling, which is shown in the overpressure
and temperature courses. The registered courses confirm the possibility of
maintaining stable overpressure with changes in the intensity of cooling.
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a)
b)
c)
Fig. 6. Courses characteristics at the overpressure of 0.2 MPa and 95% of the coolant filling
in the system: a) overpressure: 1 – small circuit, 2 – large circuit, b) temperature:
1 – entrance to the radiator, 2 – output of the radiator, 3 – output of the cylinder block,
c) coolant pump delivery
R. Krakowski, Modelling and simulation of the piston combustion engine cooling system
119
The temperature at the outlet of the engine block and the entrance to the
radiator after the assumed overpressure was maintained at 120°C. Whereas the
temperature at the outlet of the cooler ranged 95°C–115°C. Coolant pump capacity
in all cases was very similar course. To warm-up time of the system and obtain
assumed overpressure, pump capacity was almost constant and was on the level
about 32–33 dm3/min.
CONCLUSION
Currently, modelling is an important and necessary part of the research,
because it allows to solve many engineering problems at an early stage of design,
without building expensive prototypes. Modelling has special importance at the
time of the development of computers with high computing power and computer
programs for simulation.
The construction of models and then conducting simulation studies can be
carried out by building the model presented in graphical form. Then on the basis
the equation of describing the model state can be arranged, which can then be
solved. Only on this basis it is possible to simulate and analyze the results. In
addition, there are computer programs for modelling and analysis of
multidisciplinary mechatronic systems that allow you to create a model of the
system or object using block diagrams. The second method allows achieve this
goal quickly and can prevent many errors, for example in the construction of the
equations describing the model, and then solve them, because these operations are
carried out in the software simulation.
REFERENCES
1. AMESim, User's Guide Manual, IMAGINE, 5 rue Brison – 42300 Roanne – France, 1999.
2. Breedveld P., Thermodynamic bond graphs and the problem of thermal intertance, Journal of the
Franklin Institute, 1982, Vol. 314, No. 1, p. 15–40.
3. Cichy M., Modelowanie systemów energetycznych, Wydawnictwo Politechniki Gdańskiej, Gdańsk
2001.
4. Cichy M., Nowe podejście do modelowania procesów cieplnych za pomocą grafów wiązań i równań stanu, Prace Naukowe Politechniki Szczecińskiej, Szczecin 2000.
5. Kneba Z., Bond graph modelling of the new generation engine cooling systems, Journal of
KONES Powertain and Transport, 2006, Vol. 13, No. 1, p. 103–110.
6. Kneba Z., Kompleksowy model nowej generacji układu chłodzenia silnika spalinowego, Silniki
Spalinowe, SC1/2007, R. 46, s. 160–169.
7. Rosenberg R.C., Karnopp D.C., Introduction to physical system dynamics, McGraw-Hill Book
Company, New York 1983.
8. Walentynowicz J., Influence of the coolant temperature on emission of toxic compound and engine
work parameters, Journal of KONES Powertain and Transport, 2009, Vol. 16, No. 1, p. 583–590.
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STRESZCZENIE
W artykule przedstawiono pojęcie modelu i cele modelowania, następnie szerzej omówiono modelowanie graficzne, ze szczególnym uwzględnieniem grafów wiązań. W głównej części opracowania
przedstawiono modelowanie układu chłodzenia tłokowego silnika spalinowego za pomocą grafów
wiązań, w którym zaprezentowano rozwinięty model układu chłodzenia. Wykazano, że modelowanie
za pomocą grafów wiązań wymaga przedstawienia danego układu w postaci grafu, ułożenia równań
stanu opisujących model, następnie ich rozwiązania. Natomiast platforma Imagine.Lab AMESim
to oprogramowanie symulacyjne do modelowania i analizy wielodziedzinowych systemów mechatronicznych, które, po wprowadzeniu odpowiednich danych, umożliwia bezpośrednie przeprowadzenie symulacji. Następnie pokazano schemat układu chłodzenia tłokowego silnika spalinowego,
opracowany na podstawie układu chłodzenia z silnikiem o zapłonie samoczynnym 4CT90. Ponadto
opracowano model symulacyjny za pomocą schematów blokowych w oprogramowaniu AMESim.
W kolejnej części przeprowadzono symulacje w oprogramowaniu, w których wyniku wyznaczono
charakterystyki przebiegów temperatury, ciśnienia cieczy chłodzącej oraz wydajności pompy w wybranych punktach układu. Wykazano, że istnieje możliwość utrzymania założonego stałego ciśnienia
o wartości 0,2 MPa w układzie i uzyskania przy tym podwyższonej temperatury cieczy, prowadzącej
do wzrostu sprawności ogólnej silnika, co było przedmiotem dalszych badań. Uzyskane wyniki
pozwoliły stwierdzić, że oprogramowanie AMESim umożliwia rozwiązywanie wielu problemów
inżynierskich we wczesnej fazie projektowania, bez budowy drogich prototypów.