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 X = Y = f f [ X, U( )] [ X, U( )] 1 t 2 t Ẋ 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: Ẋ = f [, ( t)], 1 X U where: X state variables vector of the N elements, U excitations vector (inputs) of the M elements, Y output vector of the K elements. Y= f [ X, U ( t)], (1) 2
112 ZESZYTY NAUKOWE AKADEMII MORSKIEJ W GDYNI, nr 83, sierpień 2014 The linear form of equation (1) gives the relationship: Ẋ = A X+ B U, 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 = T S (3) KS KS KS. 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.
114 ZESZYTY NAUKOWE AKADEMII MORSKIEJ W GDYNI, nr 83, sierpień 2014 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]
R. Krakowski, Modelling and simulation of the piston combustion engine cooling system 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.
116 ZESZYTY NAUKOWE AKADEMII MORSKIEJ W GDYNI, nr 83, sierpień 2014 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: dt exp = T cinexp T airinexp (4) where: T cinexp measured temperature of the coolant at the inlet of the radiator, T airinexp measured temperature of the air at the inlet of the radiator. Heat transfer is calculated as follows: ( T T ) cinreal airinreal Qreal = Qexp dtexp seff where: Q real the actual intensity of the heat flow, Q exp experimental intensity of heat flow, T cinreal the actual temperature of the coolant at the inlet to the cooler, T airinreal the actual temperature of the inlet air to the cooler, s eff efficiency of the heat exchanger. 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: n (5) Nu = C ( Gr,Pr) (6)
R. Krakowski, Modelling and simulation of the piston combustion engine cooling system 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 h conv is then calculated based on Nusselt number as follows: h conv = Nu λ (7) c Finally, the expression for the convective heat transfer takes the form: dim d h1 = h conv c earea (T 2 T 1 ) (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 dm 3 and 9 dm 3, which represents approximately 95% and 80% in the liquid filling system, where the total system volume is about 11 dm 3. 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.
118 ZESZYTY NAUKOWE AKADEMII MORSKIEJ W GDYNI, nr 83, sierpień 2014 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 dm 3 /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.
120 ZESZYTY NAUKOWE AKADEMII MORSKIEJ W GDYNI, nr 83, sierpień 2014 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.