Propulsion Systems and Their Applications to Vehicles PDF

Propulsion systems and their applications to vehicles Notes for the course of prof. D’Ambrosio Politecnico di Torino Italy a. a. 2023-2024 Contents 1 Classification of Internal Combustion Engines 10 1.1 Introduction............................ 10 1.2 Classification of engines: Internal vs External combustion.. 10 1.2.1 Classification of ICEs in terms of layout........ 11 1.3 Main classification criteria of ICEs............... 12 1.3.1 Method of ignition.................... 12 1.3.2 Cycle duration...................... 14 1.4 Other classification criteria of ICEs............... 17 1.4.1 Air supply......................... 18 1.4.2 Mixture preparation................... 18 1.4.3 Cooling and engine shape................ 19 2 Performance of ICEs 20 2.1 Brake torque and power..................... 21 2.2 Engine work............................ 21 2.2.1 Indicated power..................... 22 2.3 Efficiency definitions....................... 22 2.3.1 Air/Fuel and Fuel/Air ratio............... 24 2.3.2 Volumetric efficiency................... 24 2.3.3 Relationships between performance parameters.... 25 2.4 Performance maps........................ 25 2.4.1 Efficiency maps...................... 26 2.4.2 Emission maps...................... 26 3 Engine balancing 27 3.1 Crank gear mechanism...................... 27 3.1.1 Mass balancing of centrifugal forces.......... 28 3.2 Engine balancing: introduction................. 28 3.2.1 Forces and moments................... 28 3.2.2 Balancing of inertia and centrifugal actions. Cyclic behaviour of the engine................. 29 3.3 Fourier analysis of the engine torque.............. 30 3.3.1 Torque in a multi-cylinder engine............ 30 3.4 Analysis of centrifugal and inertia forces............ 31 3.4.1 Centrifugal forces, four-stroke engines......... 31 3.4.2 Lengthwise layout of cranks and firing order...... 32 3.4.3 Inertial forces, four-stroke engine............ 34 1 3.4.4 Counterweights in cranks................ 36 3.4.5 Centrifugal and inertia forces, two-stroke engine... 36 3.5 Balancing of V-engines...................... 36 3.5.1 Partial rotation principle................ 37 3.5.2 Balancing of proper V-engines............. 37 4 Models of engine processes 39 4.1 Ideal heat cycle.......................... 39 4.1.1 Types of cycles...................... 40 4.1.2 Comparison between cycles............... 40 4.1.3 Over-expanded cycles.................. 43 4.2 Air-fuel cycles........................... 44 4.2.1 Cycle description..................... 45 4.2.2 Air-fuel cycle efficiency................. 47 4.2.3 Dissociation........................ 47 4.2.4 Air-fuel cycle analysis.................. 49 5 Real engine cycles 51 5.1 Heat transfer........................... 51 5.1.1 Effects of heat transfer.................. 52 5.2 Finite combustion time...................... 53 5.2.1 Spark timing and spark advance............ 53 5.3 Exhaust blowdown losses.................... 54 5.4 Crevice effect and leakage.................... 54 5.5 Incomplete combustion...................... 55 5.6 Considerations on heat transfer................. 55 5.6.1 Engine energy balance.................. 55 5.6.2 Effect of combustion chamber shape on heat transfer. 56 5.6.3 Heat transfer between burned gas and cylinder walls. 57 6 Mechanical efficiency 58 6.1 Pumping work.......................... 58 6.2 Measuring friction........................ 59 6.2.1 Mean effective pressures................. 60 6.2.2 Friction measurements methods............. 60 6.3 Total friction work........................ 62 6.3.1 Piston assembly friction................. 62 6.3.2 Friction work of inertial forces............. 62 6.3.3 Friction work of generic friction and accessory work. 62 6.3.4 Total friction work and mechanical efficiency..... 64 2 7 Gas exchange processes 65 7.1 Airflow and load regulation................... 65 7.2 Intake and exhaust processes in the four-stroke engine.... 66 7.3 Phenomena that affect volumetric efficiency.......... 66 7.3.1 Quasi-static effects.................... 66 7.3.2 Intake and exhaust system flow resistances...... 68 7.3.3 Intake system heat transfer............... 69 7.3.4 Valve timing effect.................... 70 7.3.5 Airflow chocking at intake valve............ 72 7.3.6 Intake and exhaust tuning................ 73 7.3.7 Combined effects on the volumetric efficiency..... 74 7.4 Turbocharging and supercharging................ 75 7.4.1 Mechanical supercharging................ 76 7.4.2 Wave supercharging................... 76 7.4.3 Turbocharging...................... 77 7.4.4 Volumetric efficiency of an engine with EGR..... 78 7.5 Additional considerations on flow through valves and ports. 78 7.5.1 Flow rate and discharge coefficients.......... 80 7.6 Variable valve timing and actuation.............. 81 7.6.1 Cam phasing....................... 82 7.6.2 Pumping work reduction................. 82 8 Combustion in spark-ignition engines 83 8.1 Introduction............................ 83 8.1.1 Combustion fundamentals in SI engines........ 83 8.1.2 Flame propagation.................... 84 8.2 SI engine combustion process.................. 85 8.2.1 Phases of combustion.................. 85 8.2.2 Abnormal combustion.................. 86 8.3 Thermodynamics of SI engine combustion........... 87 8.4 Analysis of cylinder pressure data................ 88 8.4.1 Maximum pressure in the cylinder........... 88 8.4.2 Heat release approach.................. 89 8.5 Combustion process characterization.............. 90 8.5.1 Parameters used to characterize combustion...... 90 8.6 Rate of reaction and burning speed............... 91 8.6.1 Rate of reaction..................... 92 8.7 Laminar burning speed...................... 93 8.8 Charge motion within the cylinder............... 93 8.8.1 Swirl............................ 94 8.8.2 Tumble.......................... 94 8.8.3 Squish........................... 95 8.8.4 Eddies........................... 95 8.9 Flame structure and turbulent burning speed......... 95 3 8.9.1 Flame structure...................... 96 8.10 Relations about flame propagation............... 96 8.10.1 Flame speed dependence on engine speed....... 97 8.10.2 Flame speed dependence on air-fuel ratio............................ 97 8.11 Dependence of efficiencies on the air-fuel ratio......... 98 8.11.1 Internal thermodynamic efficiency........... 98 8.11.2 All the efficiencies.................... 98 8.11.3 Bmep and fuel conversion efficiency.......... 99 8.11.4 Three way catalyst.................... 100 8.12 Cyclic variations in combustion................. 100 8.12.1 Partial burning and misfire............... 101 8.13 Control characteristic of SI engines............... 102 8.13.1 WOT performance characteristic of a SI engine.... 104 9 Abnormal combustion and fuel properties for SI engines 106 9.1 Definition of abnormal combustion phenomena............................ 106 9.1.1 Definition of knock.................... 106 9.1.2 Definition of spontaneous ignition and engine damage 106 9.2 Knock............................... 107 9.2.1 Pressure oscillations and audible noise......... 107 9.2.2 Transition from normal to knocking combustion.... 108 9.2.3 Knock detection..................... 108 9.2.4 Impact of knock..................... 109 9.2.5 Factors affecting knock.................. 109 9.3 Knock fundamentals....................... 110 9.3.1 Mechanisms of auto-ignition............... 110 9.4 Rapid compression machine................... 111 9.5 Analysis of auto-ignition..................... 112 9.5.1 Auto-ignition maps.................... 112 9.5.2 Chemistry of auto-ignition................ 113 9.5.3 Considerations on the auto-ignition map........ 114 9.6 Conventional fuels from crude oil................ 115 9.6.1 Volatility of liquid fuels................. 116 9.7 Fuel factors............................ 117 9.8 Motor fuels and knock rating.................. 118 9.8.1 Standard reference fuels................. 118 9.8.2 Knock rating of fuels................... 119 9.8.3 Knock suppression.................... 120 9.8.4 Effects of engine ageing................. 121 9.8.5 Commercial vehicle fuels................. 121 9.9 Knock control strategies..................... 121 4 10 Fuel metering system for SI engines 123 10.1 Mixture requirements...................... 123 10.1.1 Mixture requirements at different loads........ 123 10.2 Mixture formation approaches.................. 125 10.2.1 Fuels for SI engines.................... 125 10.2.2 Characteristics of fuels for correct mixture preparation 126 10.2.3 The carburettor approach................ 126 10.2.4 Single-point injection system.............. 127 10.2.5 Multi-point injection system............... 128 10.2.6 Fuel supply systems................... 132 10.3 Gasoline Direct Injection..................... 134 10.3.1 DI mixture preparation processes............ 135 10.3.2 GDI engine operations.................. 138 10.3.3 DI engine system components.............. 139 10.3.4 Fuel delivery in DI.................... 139 10.4 Air flow rate measurement.................... 140 10.4.1 Hot wire and hot film measurements.......... 140 10.4.2 Speed-density method.................. 140 10.5 Frequency inputs......................... 141 10.5.1 Camshaft position.................... 141 10.6 Control of the air-fuel ratio................... 142 10.6.1 Lambda sensor: HEGO................. 142 10.6.2 Lambda sensors: UEGO................. 142 10.6.3 Other lambda sensors.................. 142 11 Combustion in compression-ignition engines 143 11.1 Fundamental features of combustion in CI engines...... 143 11.1.1 Features in CI...................... 143 11.1.2 Challenges in the CI combustion chamber design... 144 11.2 Fuel injection in CI engines................... 145 11.2.1 Indirect injection system................. 145 11.2.2 Direct injection system................. 145 11.2.3 Glow plug......................... 146 11.3 Heat release rate analysis.................... 147 11.3.1 Heat release rate in direct injection systems...... 147 11.4 Fuel injection in DI engines................... 148 11.4.1 Atomization and spray penetration........... 149 11.4.2 Spray evaporation and fuel-air mixing......... 149 11.5 Ignition delay........................... 150 11.5.1 Chemical factors affecting the ID............ 150 11.5.2 Physical factors affecting the ID............ 151 11.6 Burning rates........................... 151 11.7 Conceptual model of DI diesel combustion........... 152 11.8 Multiple injection strategies................... 153 5 11.8.1 Pilot injection....................... 153 11.8.2 Post injection....................... 154 11.9 Advanced concepts of CI..................... 154 12 Fuel injection systems for CI engines and engine perfor- mance 156 12.1 Introduction............................ 156 12.1.1 Diesel fuel injection system architectures........ 156 12.1.2 Historical trend of pressure............... 157 12.2 Components in fuel injection systems.............. 157 12.2.1 Low pressure components................ 157 12.2.2 High pressure components................ 157 12.3 Pump-line-nozzle systems.................... 158 12.3.1 Delivery valves...................... 160 12.3.2 Timing device....................... 160 12.3.3 Nozzle and injector.................... 161 12.3.4 Distributor pump system................ 161 12.4 Unit injector system....................... 162 12.5 Common rail system....................... 163 12.5.1 Fuel injection....................... 165 12.5.2 Pressure control..................... 165 12.5.3 High pressure pump................... 166 12.5.4 Injectors.......................... 167 12.5.5 Solenoid system...................... 169 12.5.6 Piezoelectric system................... 170 12.6 CI engine performance...................... 171 12.6.1 Efficiency distributions with respect to air-fuel ratio. 171 12.6.2 Control characteristic.................. 172 13 Exhaust gas emissions of ICE 173 13.1 Pollution............................. 173 13.1.1 Primary and secondary pollutants........... 173 13.1.2 Air pollutants and their sources............. 174 13.1.3 Greenhouse effect..................... 174 13.2 Pollutants of ICE......................... 176 13.2.1 SI engine emissions.................... 176 13.2.2 Diesel engine emissions................. 176 13.2.3 After-treatment of exhaust gasses............ 177 13.3 Main pollutants from the ICE.................. 177 13.3.1 Carbon monoxide..................... 177 13.3.2 Hydrocarbons....................... 177 13.3.3 Nitrogen oxides...................... 177 13.3.4 Sulphur dioxide...................... 178 13.3.5 Particulates........................ 178 6 13.3.6 Ozone and smog..................... 179 13.4 Pollutant formation in SI engines................ 179 13.4.1 Effect of the air-fuel ratio................ 180 13.5 Pollutant formation in CI engines................ 180 13.6 Kinetics of Nitrogen compounds................ 181 13.6.1 Nitrogen dioxide..................... 181 13.7 Influence of engine parameters on emissions.......... 182 13.7.1 SI engines......................... 182 13.7.2 Diesel engines and particulate characteristics..... 183 13.8 Exhaust gas recirculation.................... 184 13.8.1 Low and high pressure EGR............... 184 13.8.2 Influence of EGR in diesel engines........... 184 13.9 After-treatment systems..................... 185 13.9.1 After-treatment for SI passenger cars.......... 185 13.10Emission control regulations................... 187 13.10.1 Emission regulation testing in the EU......... 187 13.10.2 Testing method: CVS dilution............. 188 13.10.3 Real driving emissions.................. 189 13.10.4 Carbon dioxide emission regulations.......... 189 13.10.5 Emission control for heavy-duty vehicles........ 190 14 Cooling systems 191 14.1 Introduction............................ 191 14.1.1 Overheating of the engine................ 191 14.1.2 Cooling system components............... 192 14.1.3 Historical evolution of cooling systems......... 193 14.2 Heat transfer in the cooling system............... 193 14.2.1 Combustion gasses to coolant.............. 193 14.2.2 Coolant to external air.................. 194 14.2.3 ATB index........................ 194 14.3 The coolant............................ 195 14.3.1 Water and glycol characteristics............ 195 14.4 Radiator.............................. 196 14.4.1 Horizontal coolant circulation.............. 197 14.5 Coolant pump........................... 197 14.5.1 Cavitation......................... 197 14.6 Thermostat............................ 198 14.6.1 Conventional wax thermostat.............. 198 14.6.2 Characteristic temperature curve of the thermostat.. 199 14.7 Expansion reservoir and pressurization cap.......... 201 14.7.1 Importance of pressurization.............. 201 14.7.2 Gas deaeration (degassing)............... 201 14.7.3 Circuit filling....................... 202 14.7.4 Pressurization cap.................... 202 7 14.7.5 Closed cooling system.................. 202 14.8 Fan................................. 203 14.8.1 Position of the fan.................... 203 14.9 Oil heat exchangers........................ 204 14.9.1 Plate coolant-to-oil heat exchanger........... 204 14.9.2 Air-to-oil heat exchanger................ 204 14.10Intercooler............................. 204 14.10.1 Air-to-air intercooler................... 205 14.11Exhaust Gas Recirculation.................... 206 14.11.1 High pressure short route EGR............. 206 14.11.2 Low pressure long route EGR.............. 206 14.12Cooling system design and dimensioning............ 207 14.12.1 Fan dimensioning..................... 208 14.13Experimental tests........................ 208 14.13.1 Hear transfer rate to the coolant............ 208 14.13.2 ATB index measurement................. 208 14.14Advanced Cooling Systems................... 209 14.15Thermal management...................... 209 14.15.1 Metal temperature measurement............ 210 14.15.2 Development of mechanical coolant pumps...... 210 14.15.3 Thermostat improvement................ 212 14.15.4 Engine downsizing.................... 214 14.15.5 Increase of charge air heat load............. 215 14.15.6 Cooling systems with two cooling loops........ 215 14.15.7 Cylinder head integrated exhaust manifold...... 216 15 Installation of elements in the engine compartment 219 15.1 Powertrain configurations.................... 219 15.1.1 Powertrain configurations................ 219 15.1.2 Front transverse engine................. 220 15.2 Intake line in the engine compartment............. 220 15.2.1 Filter........................... 221 15.2.2 Minimization of load losses............... 221 15.2.3 External air pick-up point................ 222 15.2.4 Air flow meter...................... 222 15.3 Engine compartment heat exchangers............. 222 15.3.1 Engine oil heat exchangers............... 223 15.3.2 Transmission oil heat exchanger............. 223 15.3.3 Intercooler........................ 223 15.3.4 Further considerations.................. 224 15.4 Air passage through engine compartments........... 224 15.4.1 Active grille shutters................... 225 15.5 Heating, ventilation and air conditioning............ 226 15.5.1 Air distribution through the interior cabin....... 226 8 15.5.2 Temperature control................... 226 15.5.3 Boost of heating systems................ 226 15.5.4 Refrigerant circuit with expansion valve........ 227 15.5.5 R744-based refrigeration cycle.............. 228 16 Engine-vehicle matching 229 16.1 Introduction: longitudinal dynamics.............. 229 16.1.1 Lumped parameter model................ 229 16.1.2 Main equations of longitudinal dynamics........ 229 16.1.3 Acceleration and forces due to inertia......... 231 16.1.4 Traction force at the wheels............... 232 16.1.5 Transmission efficiency.................. 233 16.2 Vehicle performance and performance index.......... 234 16.3 Coastdown method........................ 235 16.3.1 Dissipation forces in the transmission......... 235 16.3.2 The coastdown approach................ 235 16.3.3 Various coastdown procedures.............. 236 16.3.4 Vehicle homologation through coastdown method... 239 16.3.5 Coastdown implementation on a test rig........ 240 16.4 Gear ratio selection........................ 241 16.4.1 Gear ratios selection................... 242 16.4.2 Overall gear ratio..................... 243 16.4.3 Selection of the intermediate gears........... 245 16.5 Vehicle fuel consumption..................... 247 16.5.1 Fuel consumption simulation.............. 247 16.5.2 FC simulation: direct approach............. 248 16.5.3 Considerations on FC maps............... 249 16.5.4 Fuel consumption and emissions............ 249 16.6 Matching of transmission to engines.............. 249 16.7 Influence of driving style on fuel consumption......... 249 16.7.1 Rule 1........................... 250 16.7.2 Rule 2........................... 251 16.7.3 Rule 3........................... 251 16.7.4 Rule 5........................... 251 16.7.5 Further considerations on ECO-DRIVE........ 251 16.7.6 FIAT eco:Drive...................... 251 9 Classification of Internal Combustion Engines 1.1 Introduction The vehicle propulsion is usually obtained by means of engines. An engine is a mechanical device that can convert the chemical energy of a fuel into mechanical energy available at a rotating shaft. The chemical energy is first converted into heat through combustion and then the heat is converted into mechanical work by means of a working medium. QLHV −→ Wb The subscript ”LHV” stands for lower heating value, which is a value specific to every fuel, measured in laboratory. The subscript ”b” instead, stands for brake. It comes from the way in which we measure the engine’s torque or power: we connect the output shaft to a brake. 1.2 Classification of engines: Internal vs External combustion Engines can be divided into two families: internal combustion engines (ICE) and external combustion engines (ECE). In ICEs the combustion occurs inside of the machine and the fluid which performs the cycle changes its properties. The fluid inside of the cylinders is changed and so it has to be periodically )each cycle) replaced by new fluid (which is usually air and fuel). The cycle is open. In ECEs, the combustion happens in a separate chamber, called burner while the power generation occurs in another element which receives heat from the burner. The working fluid does not have its properties altered (it is not burned) and it does not need to be changed every cycle. Examples of ECEs are the Stirling engine and steam engines. N.B. Turbines have the combustion happening in a burner, but the fluid changes properties (it takes part in the combustion). 10 1.2.1 Classification of ICEs in terms of layout Internal combustion engines can be of two types: rotary or reciprocating. The rotary (Wankel) engine has very limited automotive applications, so it will be briefly described and then it will be set aside. The only automotive application was created by Mazda. It is very compact and there is a rotor that replaces the crank mechanism. The rotor moves in an oval housing. Problems with this engine were the fact that some sides of it were always hot and others always cold. In addition to this, the pollution generated by this engine was pretty high. Reciprocating engine The reciprocating engine is made by some cylinders in which an el- ement called piston can move up and down. A crank-slide mech- anism connects the piston to the shaft. The rod attached to the pis- ton is the connecting rod (con- rod) while the rod connecting the conrod to the shaft is the crank. A shaft connects different cranks, so it is called crankshaft.The engine is re- ciprocating because when a piston goes up, another goes down. The upper position of the piston is called top dead centre (TDC), while the lowest position of the piston is called bottom dead centre (BDC). The volume that we have at TDC is the minimum volume of the cham- ber an it is sometimes called clear- ance volume, Vc. The volume at BDC is the maximum volume of the chamber. The difference in volume Figure 1.1: Reciprocating engine between maximum and minimum is called displacement (cilindrata), Vd. The total displacement of an engine is Vd times the number of cylinders, i. We can also define a quantity called volumetric compression ratio: rc = VVmax min. The value of the distance between TDC and BDC is called stroke, s = xT DC − xBDC ≈ 2r, where r is the length of the crank. The equality is not always true since the crank might have an offset. The diam- 11 eter of the cylinder is called bore, B. So the displacement is: πB 2 Vd = s 4 1.3 Main classification criteria of ICEs ICEs are devices in which a fluid (air and fuel mixture, called charge) generates work by go- ing through a process of combus- tion. The fuel reacts with an oxidizer (air: 79.05% N2 , 20.95% O2 and some other elements like Ar, CO2 ,...). These two reac- tants produce product and heat. The heat increases the pressure in the chamber and said pres- sure acts on the top of the pis- ton. M = Ft r = Fc b is the instantaneous torque. Since the pressure on the piston varies instant by instant, also Ft and M do. The torque produced by the engine is defined as the mean value of the instantaneous work. There are several ways to classify ICEs, but the two main ones are: method of ignition: spark or compression ignition; Figure 1.2: Forces on the piston cycle duration: two or four strokes. 1.3.1 Method of ignition There are two ways of igniting the charge. Spark ignition (SI) In spark ignition the fuel is a low reactivity one, when in vapor form. It is so little reactive that the mixture of fuel and air has to be ignited by means 12 Figure 1.3: Spark ignition of the addition of energy (spark). This allows us to pre-mix air and fuel in a chamber, before the occurrence of the combustion. The charge is then injected into the cylinder and this injection type is called port injection. Inside of the cylinder, the spark plug creates an electrical discharge at the proper moment, igniting the combustion. The temperature increases and the reaction starts. There is then a flame propagation from the ignited part of the charge to the other unburned parts of gas. A very unwelcome event is the self-ignition of parts of gasses that already have a high temperature and pressure and ignite before the flame reaches them. These parts are called end gas and they are located close to the pis- ton. Because of the upward motion of the piston and because of the expan- sion of the already burned gas, their temperature and pressure rise, causing a self-ignition. This generates an abnormal combustion, called knock. The term knock comes from the sound produced by this abnormal combustion. In order to avoid these kinds of abnormal combustion we have to: use the proper fuel (Octane number over 95) limit the maximum pressure by limiting the compression ratio rc = (8 − 12) The fuel for SI engines is called gasoline. The mass of fuel has to be in an almost constant ratio with the mass of air at all times. if we wanted to reduce the torque (in general, the power) we would need to reduce the mass of fuel that is delivered to the cylinder. In order to keep the mass of fuel to mass of air ratio constant, we would need to reduce the delivered mass of air as well. The device that has the task of controlling the amount of air in that gets delivered to the cylinder is the throttle valve, which is inside the intake line. The valve reduces the mass of air per cycle per cylinder, ma. Basically, it reduces the air mass flow rate: ṁ = maa inc 13 n The term i is the number of cylinders, while nc = m , where m is the number of revolutions per cycle (1 for a two-stroke or 2 for a four-stroke) and n is the engine speed in [rps]. Compression ignition (CI) The fuel used for CI is a very reactive one in vapor form (diesel oil). Since it is very reactive, we do not pre-mix it with air before the combustion. Instead, we push air in the combustion chamber and then the fuel is injected (by devices called injectors) a few moments before the combustion.The high values of T and p activate the reaction of the fuel. The combustion occurs around the fuel and there will be no flame propagation. a small part of the fuel reacts first (pre-mixed combustion) and then the main combustion happens (diffusive combustion). In CI engines: the fuel has to be able to self-ignite very well (Cetane number); the compression ratio can be larger than the one for SI engines: rc = (14 − 22) In Diesel engines, since the fuel is injected in the air only before the com- bustion, there is no need to have a constant ratio between mass of fuel and mass of air. So, if we wanted to reduce the engine power, we would just need to reduce the mass of fuel. N.B. Diesel oil is much ore volatile than gasoline. 1.3.2 Cycle duration When we talk about cycle duration, we are referring to the number of strokes of the piston that are necessary in order to complete a cycle. Usually two strokes of the piston make a revolution of the crank. If the cycle is completed in one revolution, the engine is a two-stroke engine. If instead the cycle is completed in four revolutions, the engine is a four-stroke engine. The latter is the most used in automotive applications. Four-stroke engine The cycle of this type of engines is completed in two revolutions (four strokes) and it is composed by six phases (or only five if we put the last two phases together). Let us now examine the six phases, referring to Fig- ure 1.4: Intake phase: it correspond to the first stroke. The piston moves down to BDC and the intake valve is open. Fresh charge is drawn in the cylinder. In order to maximize the mass inducted, the inlet 14 Figure 1.4: Clapeyron diagram for the four-stroke engine valve opens shortly before the stroke starts and closes slightly after it ends. The mixture is drawn inside by the pressure difference between ambient and cylinder. The exhaust valve is closed (6I −→ 1); Compression phase: both valves are closed and the piston moves upwards towards TDC. The volume of the chamber decreases and the pressure increases. The phase is shorter than the stroke (1 −→ 2); Combustion phase: the combustion is initiated before the piston reaches the TDC and ends with the piston already descending (2 −→ 3); Expansion (or power) phase: the piston is pushed down by the extreme pressure in the chamber. this is the phase in which we produce mechanical power (3 −→ 4); Exhaust phase: as the piston approaches the BDC, the exhaust valve opens and the spent gas is first pushed out by the pressure differential between the chamber and the outside (blowdown phase, 4 −→ 5). When the piston reaches the BDC, the blowdown finishes and the displacement part of the exhaust phase begins: the piston completes a full stroke to displace out the remaining exhaust gas (5 −→ 6E ) In Figure 1.5 we can see the timing of the various phases with respect to the crank position. Notice that α1 > α2. Notice how the combustion starts slightly before we are at TDC and ends after we passed TDC. this is done to maximize torque. The moment at which both intake and exhaust valves are open at the same time is called valve overlap. 15 Figure 1.5: Valve timing diagram for the four-stroke engine Two-stroke engine In the two-stroke engine, the cycle is completed in only one revolution. Instead of the valves, we have some ports, which are opened and closed by the piston covering or uncovering them. This design needs a way to pressurize the charge in order to make it flow inside of the chamber which is at ambient pressure. Let us now examine the six phases: Intake (or charge) phase: the exhaust port is closed and fresh charge enters the cylinder; Compression phase: inlet and outlet ports are closed and the piston goes upwards, reducing the volume and increasing the pressure; Combustion phase: towards the end of the compression phase, the combustion starts; Expansion phase Exhaust phase: the piston goes down because of the expansion and it uncovers the exhaust port (which is higher than the intake one). The gasses start to exit because of the blowdown; Scavenging phase: the piston goes down more and it uncovers the intake port. The fresh charge displaces the exhaust gasses outwards. Since the exhaust port is higher than the inlet one, in order to keep the charge flowing in when the piston goes up again (to start the next cycle) and covers the inlet, we have a controlled charge valve that is open until the exhaust port gets covered by the piston. The scavenging phase coincides with part of the intake phase. 16 Figure 1.6: Valve timing diagram for a two-stroke engine As we said before, we need a device that pressurizes the air that goes into the intake port, so that pi > pe > pe. We can use a mechanical (volumetric) compressor like the Roots compressor or a turbocompressor to do that, but the cheapest and simplest solution is to use the crankcase as a compressor. A one way valve (Reed valve) is inserted on the side of the crankcase. When the piston goes up, the pressure inside of the crankcase is reduced and the valve opens, letting the charge inside. When the piston goes down, the volume of the crankcase is reduced and the valve is closed. The charge is pressurized and gets pushed to the intake port. Two vs four stroke engines The four-stroke engine takes double the revolutions of the two-stroke one to complete a cycle, so its power output should be half of the two-stroke’s one. In reality, the volumetric efficiency of the two-stroke engine is worse than the four-stroke’s one. Even tough the two-stroke has a more compact design and a high regularity of torque, the low efficiency and high emissions (due to the fact that some of the fresh charge is pushed in the exhaust port along the exhaust gasses) are very big disadvantages. The two-stroke is not used in automotive applications, but its compactness makes it very useful for small power units (like ones for chainsaws, small electric generators,...). Big diesel two-stroke engines are used to power large propulsion plants (ships, large electric generators,...) because of their simple structure. Thermal and mechanical drawbacks of these engines are more easily controlled in large engines. 1.4 Other classification criteria of ICEs There are other less relevant methods of classification for ICEs. 17 1.4.1 Air supply ICEs need air to work. We can classify the engines with respect to the way air is delivered to them: naturally aspirated: there is no compressor that delivers air to the engine; supercharged: there is a mechanical compressor that delivers air to the engine. The compressor is moved by the engine; turbocharged: there is a turbocompressor (turbine coupled to a com- pressor) taht delivers air to the engine. The turbine is spun by exhaust gasses coming from the engine. Why would we want to deliver compressed air to the engine? The answer is pretty simple: a larger air density means that we can deliver a larger mass of air. Usually we place an intercooler between compressor and engine in order to reduce the fluid’s temperature thus increasing its density even more. p ρ= RT 1.4.2 Mixture preparation This classification method ha to be combined with the SI versus CI one. It basically classifies these two categories of engines by the way the mixture is prepares. For SI engines we have: carburettor: used up until the 90’s. The air passe through a Venturi throat, connected to a fuel reservoir (the air scoops up some fuel). The carburettor does not allow for precise control; port fuel injection: an injector places a certain amount of fuel inside of the air just before the inlet valve; direct injection: the injection takes place inside of the cylinder and has to be performed in large advance with respect to the combustion in order to allow the mixture to be formed. For CI engines we have instead: indirect injection: it takes place in a chamber before the entrance of the cylinder and it is valid only for small displacement engines. Efficiency losses are present; direct injection: the injection takes place inside of the chamber. 18 1.4.3 Cooling and engine shape The last two ways to classify ICEs are method of cooling (liquid with a cooling line and a radiator or air cooling) and shape of the engine (in-line, V-engine and opposite cylinder engine). 19 Performance of ICEs When we examine the performance of an ICE, our interest is in its perfor- mance over is whole operating speed range, its efficiency and fuel consump- tion and its emission characteristic. The performance is defined by the torque, the power and the speed of the engine. We can define: The maximum power available at each speed within the useful en- gine operating range. This value is also called full load or wide-open throttle (WOT) power; The range of speeds and powers over which the engine’s operation is satisfactory. Some other useful parameters are the rated speed, which is the speed (of the engine) at which we have the maximum power and the maximum speed, which is the maximum engine speed at which we can go without damaging the engine. Usually the maximum speed is larger than the rated one. Diesel engines have a higher torque over a lower speed range (max Figure 2.1: Full load torque and power of a turbocharged diesel engine 4000-4500 rpm), while SI engines have a lower torque over a wider speed range (max 6000-7000 rpm). 20 2.1 Brake torque and power The engine torque is measured with a dynamometer, also called brake. This device absorbs me- chanical power coming from the en- gine. The engine’s crankshaft is connected to the brake’s rotor. The rotor is somehow coupled with a sta- tor (mechanically, electromagneti- cally,...) which is supported by low friction bearings. The engine drives the rotor, which in turn tries to drive the stator. The torque exerted Figure 2.2: The dynamometer on the stator in order to keep it still, while the rotor spins, is evaluated considering the force measured by a load cell. T = F · b and Pb = T · ω = T · 2πn. We can evaluate the power of the engine either using the International Sys- tem (Watts) or by using the thecnical system (horsepower). Notice how the European thecnical system is different from the American or British one. 1CV = 1P S = 75kgf m · rad s = 735.499W (cavallo vapore); 1HP = 550lbf · f t · rad s = 745.6999W (horsepower) 2.2 Engine work The work is produced inside of the cylinder because of the pressure of the gas that pushes the piston downwards. Pressure data for the gas in the cylinder is measured by a pressure transducer. We can plot the engine cycle in a p-V diagram. The indicated work per cycle (per cylinder) is obtained through integration along the cycle line: I p dV In two-stroke engines, the application of this work formula is pretty straight- forward. In four-stroke engines, instead, we have two different kind of indi- cated works (areas referred to Figure 2.3): Gross indicated work per cycle: Wig. It is the work delivered to the piston over compression and expansion strokes (area A + area C with sign, for NA engines); Net indicated work per cycle: Win. It is the work delivered to the piston in the entire cycle (area A - area B, for NA engines) 21 Figure 2.3: Work cycles in engines The sum of A and C is the work transfer between the piston and the cylinder gasses during intake and exhaust phases and it is called pumping work. This work is negative in naturally aspirated engines, since the intake pressure is lower than the exhaust pressure. In supercharged or turbocharged engines, it is possible to have pi > pe and so we can have the pumping work as a positive quantity. We cannot use this configuration with SC and TC engines since due to the EGR (exhaust gas recirculation) regulations we need to have pi < pe. This regulation is used to reduce the N Ox gasses released into the atmosphere by the combustion in the chamber (oxygen combines with nitrogen in the chamber due to high temperatures). Basically we send a part of the exhaust gasses into the intake port so that the charge will be diluted by them. This creates a slower combustion with lower temperatures, thus reducing the chance of N Ox formation. We send these gasses via pressure differential, hence the need to have pi < pe. 2.2.1 Indicated power We can define the indicated power as: Wi · i · n Pi = m The indicated power is the sum of the brake power and of the power that is lost due to friction in the engine, driving the engine accessories and the pumping power (only when we consider the gross indicated power). So, Pig = Pb + Pf 2.3 Efficiency definitions There are several useful values that we can consider. 22 Mechanical efficiency It is the ratio of the brake power (useful power) and of the gross indicated P power: ηm = pPigb = 1 − Pigf Typical mechanical efficiencies are around 90% at low speeds and around 75% at maximum rated speed. In idle conditions it is equal to zero. Mean Effective Pressure It is a way to compare engines regardless of their displacements (bigger displacement means larger torque). It is defined as: W mep = Vd Pi m We can have the indicated mep and the brake mep: imep = iVd n and Pb m T 2πm bmep = iVd n= iVd.The imep represent the area of the cycle (summing areas with sign). Even tough it isnot a pressure physically speaking, it has the units of a pressure mJ3 = P a. Specific fuel consumption and efficiency n The specific fuel consumption is the fuel flow rate ṁf = mf i m divided by m˙f m˙f the power output. We can have: isf c = Pi and bsf c = Pb , measured in g/kW h. Low values of sfc are desirable. We can define the brake fuel conversion efficiency, which is the value that tells us how much of the fuel’s energy is actually converted into power: Pb Wb ηf = = ṁf QLHV mf QLHV The term QLHV represents the lower heating value of the fuel which is a measure of its energy. Notice that bsf c = ηf Q1LHV. We can also have an indicated fuel conversion efficiency: Wi ηi = mf QLHV Specific power Pb,max iVd 23 2.3.1 Air/Fuel and Fuel/Air ratio One of the most important parameters when it comes to defining the engine operating conditions is the Air/Fuel ratio. It is defined as: ṁa ma α= = ṁf mf We are usually interested in normalizing this ratio with respect to the stoi- chiometric ratio, which is the Air/Fuel ratio in stoichiometric conditions (we have the amount of air that we need in order to burn a kilogram of fuel): α λ= αst Considering instead the Fuel/Air ratio, we have: 1/α ϕ= 1/αst We can evaluate the stoichiometric ratio by considering the reaction between fuel and oxygen: b b b Ca Hb + (a + )(O2 + ψN2 ) −→ aCO2 + H2 O + (a + )ψN2 4 2 4 nN2 79 where ψ = nO2 = 21 = 3.77. So we can define the stoichiometric ratio: 2a(a + 4b )ψMN + 2(a + 4b )MO αst = aMC + bMH For both gasoline and diesel, values of this ratio are around 14.6. We can define the energy content of a quantity of fuel by using mf ·QLHV. If we are in stoichiometric conditions, we can define the so called energy parameter: QLHV αst. Notice how, for instance, hydrogen has a very high lower heating value but also has an high stoichiometric ratio. This means that its energy parameter is not that much higher than the one of other fuels. 2.3.2 Volumetric efficiency The intake system restricts the amount of air that can be inducted inside of the engine. We use a parameter called volumetric efficiency in order to measure how effective the engine is at removing burnt gasses and at inducting new charge. This parameter is only used in four-stroke engines since they have a distinct induction (intake) phase. It is defined as the the actual mass of air inducted divided by a reference mass of air: ma ma ṁa λv = = = ma,ref ρa Vd ρa iVd n2 24 The reference air density that we should consider depends from the type of air supply. In fact, for naturally aspirated engines, we choose the ambient air density while for supercharged or turbocharged engines we choose the air density of the air in the intake manifold. In this way we can see how much air we have in the cylinder with respect to the air that we have in the manifold (we measure losses inside the induction circuit). 2.3.3 Relationships between performance parameters ima n λv ρa iVd n/2 Pb = ηf ṁa QLHV = ηf QLHV = ηf QLHV (2.1) α m α Wb Pb bmep = = (2.2) Vd iVd n/2 By combining Equation 2.1 and Equation 2.2, we get λv ρa QLHV bmep = ηf (2.3) α We can also say that Pb = T ω = T · 2πn (2.4) And so, 4πT bmap = (2.5) iVd From these equations we can see that in order to increase the power, we have to increase ηf or λv or by having fuels with an higher QLHV. Also, an high volumetric efficiency means low pressure losses. In order to increase the power we can increase the speed. 2.4 Performance maps The wide-open throttle condition is not always reached (almost never reached) so we need to be able to understand how much torque we have in other conditions. When the throttle is not fully open, the max- imum torque reached is lower and the peak is situated at lower speeds. Obviously the speed plays its part (lower torque at higher speeds). No- tice how the throttle valve is never fully closed. This is because we need some fuel to be delivered in order to keep the engine running at idle con- Figure 2.4: Influence of throat angle dition. on torque 25 Figure 2.5: Fuel consumption efficiency map 2.4.1 Efficiency maps There are several efficiency maps that we can use, one for each efficiency type. We have an important re- lationship which is: ηf = ηi ηm. The efficiency that we are mostly interested in is the fuel consumption efficiency (Figure 2.5). We can notice an ”eye” in the map, in which we can find the maximum of the efficiency. Along with efficiency maps, we have fuel consumption maps, which indicate the fuel consumption of our engine in a bmep-engine speed plane. In the bsfc map we can see a maximum at low-medium engine speed and medium-high loads. 2.4.2 Emission maps Lastly, we have emission maps. We have maps for most of the gasses that are emitted by the engine (HC, CO, N Ox ,...) 26 Engine balancing In an engine, the pressure of gasses inside of the cylinder is used to create torque, through the crank-slide mechanism, which can be referred to as the crank gear. 3.1 Crank gear mechanism The crank gear is the mechanism that transforms the reciprocating motion of the piston into a rotating motion of the shaft. We have that the piston is a reciprocating mass, the crank a rotating mass, while the conrod is a mass that has a motion in-between a reciprocating and a rotating motion. The forces needed to accelerate and decelerate the masses, are the iner- tia forces. The pressure forces act- ing on the piston are translated in a force which acts perpendicularly to the surface of the piston. This force can be decomposed in a force paral- lel to the conrod (Fconrod ) and one force parallel to the piston surface (FN ). The force acting on the con- rod is then transmitted to the crank as the vector sum of a force tangen- tial to the direction of rotation of the crank (FT ) and a force radial to the direction of rotation (FR ). The tangential force, combined with the radius of the crank gives us (instant by instant) the instantaneous engine torque: Meng = FT · r. The radial force, instead, does not contribute to torque generation and it is com- pensated by the crankshaft bear- ings. Obviously, the engine block has to be able to compensate for Figure 3.1: The crank gear the engine torque, through a reac- tion torque, which is the product of the normal force acting on the piston, 27 multiplied by the distance of the point of application of this force from the centre of rotation of the crankshaft: Mreaction = FN · b. Two forces arise in the engine restraining system in order to compensate for this reaction torque. 3.1.1 Mass balancing of centrifugal forces Rotating masses produce centrifugal forces which are unwelcome. Fortu- nately, they are also fairly easy to balance by using counterweights that produce the same amount of centrifugal force of the rotating masses, but in opposite direction. 3.2 Engine balancing: introduction The aim of engine balancing is to eliminate or at least attenuate the vibra- tions that come from all of the stresses that the engine block is subjected to. Notice that these vibrations are then transmitted through the whole structure. 3.2.1 Forces and moments Forces acting on the engine frame There are several forces that act on the engine frame: we have the sur- face forces that the engine exchanges withe the mounts, the torque that the engine exchanges withe the outside through the crankshaft, the forces ex- changed with engine accessories and forces acting on the engine when it is fitted on the vehicle (clutch,...). Forces acting on the engine The forces due to gas pressure are already compensated by the crank bear- ings, so they are not transferred to the frame. The weight is a constant force and so does not influence vibrations. The last two forces that we need to consider are the reciprocating inertia motions (constant in direction, vari- able in magnitude) and centrifugal (inertia) forces, which are constant in magnitude and varying in direction. Moments along the crankshaft axis We have several moments acting on the axis of the crankshaft. Obviously, we have the engine torque, which is due to the pressure forces of the gas on the piston, summed up withe the inertia forces of the piston itself. We also have the inertial torque, which are dependant from the crank position and is a result of the inertia of the crank and conrod: Mi,e = Ie · ω̇. Since 28 the conrod has a reciprocating and a rotating part, we calculate its inertia moment by using a schematic representation of the rod. Schematization of the connecting rod The connecting rod has a part (con- nected to the piston) which has a certain mass and a part connected to the crank with another mass. In between there is a distributed mass. The conrod is approximated as two concentrated masses mA and mB , withe the centre of gravity placed as in Figure 3.2. In reality, we need to consider the fact that different distances from G generate different inertia moments so, in order to be consistent with the reality, the over- all inertia moment of the conrod will be corrected by adding the term I0 < 0: Irod = mA x2A + mB x2B + I0 Figure 3.2: The conrod The term I0 is called the ”on frame correction of the rod inertia” Moments acting perpendicularly to the crankshaft axis There are also moments which act perpendicularly to the engine. These mo- ments are caused by the inertia forces (of the pistons) and by the centrifugal forces. 3.2.2 Balancing of inertia and centrifugal actions. Cyclic behaviour of the engine Our goal is now to balance all actions due to inertia and centrifugal forces. We want the forces on the engine mounts to be balanced (resultant equal to zero) and the moments acting on the mount to be balanced (resultant equal to zero) as well. Another important accomplishment in engine balancing is the regularity of engine torque. The engine behaves in a cyclic way. The tangential force that creates the engine torque is in fact a cyclic force that depends from the crank position. In Figure 3.3, we have the tangential pressure (tangential force divided by piston area) as a function of crank angle (the zero is positioned at TDC of combustion phase). 29 Figure 3.3: Cyclic behaviour of the engine 3.3 Fourier analysis of the engine torque A very important tool in the analysis of the engine torque is the Fourier analysis, which allows us to decompose the engine torque in all of its har- monics. The torque produced by a single cylinder can be defined as: Msingle = M0 + Σk Mk sin(kωt + ψk ) Where M0 is a constant average torque and Mk is the magnitude of the k th harmonic. 3.3.1 Torque in a multi-cylinder engine In order to get a smooth torque at the crankshaft, we should not have all cylinders firing at the same moment. Actually, we want the engine to be in an evenly spaced cranks. In fact by tweaking the crank position with respect to a reference one, we can get a different firing order of the cylinders. We have a formula to get the phase shift of each crank with respect to a reference one: m m ∆φ = 2π = 360◦ i i For example, a four-stroke, four cylinder engine will have a phase shift of 180◦ for each crank. The resulting moment of the engine is obtained by properly sum up all contributions of all cylinders, taking the phases into account. The phase of the cylinder next to fire with respect of the first to fire is: φj = ∆φ(j − 1). The overall torque can be then written as: Mmulti = Σj Mj = iM0 + Σij Σk Mk sin(kωt + ψk − δjk ) 30 Figure 3.4: Tangential pressure for a four cylinder engine With δjk = k∆φ(j − 1). We can identify the principal harmonics by identifying the harmonics in which all torque vectors sum up (we basically sum up the same harmonic through all cylinders). Another important thing to keep in mind, is the fact that for an in-line engine, with evenly spaced cranks, the torque vectors sum up when the harmonic is a multiple of i/2 and cancel each other out when the harmonic is not a multiple of i/2. For a multi- cylinder engines, we can choose to only consider the principal harmonics (p) and say that: Mmulti = i[M0 + Σin/m Mp sin(pωt + ψp )] Obviously we are supposing that each cylinder has the same torque output for a given crank position, but in reality this is obviously not real. So at all harmonics we will have a certain amount of torque. 3.4 Analysis of centrifugal and inertia forces We are now interested in analyzing the contribution of centrifugal and inertia forces. The centrifugal forces are written as: FC = −mc ω 2 r. The inertia forces can be written as a Taylor expansion: Fa = −ma ẍ = −ma ω 2 r[cos θ + λ cos 2θ +...], where λ = r/l is the conrod ratio. 3.4.1 Centrifugal forces, four-stroke engines We can use the so-called star diagrams in order to understand the position of the pistons (up or down) in order to see if the centrifugal forces are balanced or not. We can clearly see that apart from the four-stroke two cylinder engine, the centrifugal forces are automatically balance. It is important 31 Figure 3.5: Star diagrams for two and four stroke engines to notice that even tough the centrifugal forces are always balanced, the moments that they create might not be balanced as well. 3.4.2 Lengthwise layout of cranks and firing order In order to balance the moments produced by the centrifugal forces, we need to make sure to have the firing cylinders in a certain position with respect to the ones that are not firing.We also need to determine the firing order. We can number the cylinders according to standards: they are numbered consecutively, in the order in which they would be intersected by an imagi- nary reference plane. We usually start from the opposite side of the power output. The plane is located to the left and the numerical assignments then proceeds clockwise along the longitudinal axis of the engine. If there are more cylinders on the same plane, they will be numbered starting from the closest to the observer. Regarding the firing order, the rule is to try not to have two consecutive cylinders firing at once (not always possible). Let us see a couple of exam- ples. Four-stroke engine, i even Let us consider a four cylinder engine. The position of the pistons must be a symmetrical lengthwise layout, relative to the middle of the crankshaft. This means having two pistons on opposite sides of the middle of the crankshaft at the same height at the same time.In this way the moment produced by the centrifugal forces acting on the pistons will be zero. Regarding the firing order, we can start from firing cylinder 1, then we need to fire a cylinder which was at BDC (2 or 3), so we choose 3 in order not to have two con- secutive cylinders firing at once. Then we go with 4 and, in the end 2. We restart from one. The order is: 1-3-4-2-1-... Another equivalent order is 1-2-4-3-1-... 32 Figure 3.6: Symmetric lengthwise layout Four-stroke engine i=2 This is a special case of the family of configurations discussed above. Since there are only two cylinders, we can balance the momentum by adopting a symmetrical lengthwise layout, but we cannot balance the centrifugal forces. This in why we need to add a counterweight of equal mass of the cylinders whose centrifugal force will balance the one produced by the cylinders. Four-stroke engine, i odd In case of an odd number of cylinders, the best layout in order to minimize (but never fully cancel out) the momentum is the anti-metric lengthwise layout of cranks. The principle of this layout is to position the middle cylinder at the top, then the two close to it and then the outermost ones in swapped positions. In Fig- ure 3.7 we can see an example of this principle for a five cylinders en- gine. If thee were more cylinders, we would swap only the two furthest ones. We can clearly see that the moment resultant is not zero, but it certainly is reduced with respect to the standard layout. A three cylinder engine is the only one that cannot be adjusted with this layout Figure 3.7: Anti-metric layout for a and needs counterweights. Regard- five cylinders engine ing the firing order, we still use the 33 aforementioned rule. 3.4.3 Inertial forces, four-stroke engine The inertial forces can be expressed as Fa = −ma ẍ ≈ −ma ω 2 r[cos θ + λ cos 2θ +...] Since the terms of higher harmonics (we take the coefficient of the θ as the order of the harmonic) get smaller and smaller, we will consider only the first ′ two, defined as: Fa = −ma ω 2 r cos θ which varies periodically synchronous ′′ to the shaft speed and Fa = −ma ω 2 rλ cos 2θ, which varies periodically twice per shaft revolution. The first and second order forces display a variable modulus and a constant direction. We can decide to reduce these forces to an equivalent field, made up of two rotating vectors of constant modulus equal to half of the value of the force. The sum of the two vectors is the actual force, since the vectors rotate in opposite directions. In this way we can analyze inertial forces as we did with centrifugal forces. First-order forces ′ At each angle step, the force Fa is the resultant of two symmetrical forces with constant modulus that rotate with ω and −ω respectively. The two force fields are equivalent to the cen- trifugal forces rotating at crankshaft speed in the two directions. We ′ can define Fa1 as the first order force rotating n crank direction and ′ Fa2 as the first order force rotating in opposite crank direction (contra- rotating force). For in-line engines, ′ if the system of Fa1 forces cancels ′ out, so will the system of forces Fa2. Figure 3.8: First-order force This is not true for V-engines. Second-order forces ′′ As we did for the first order forces, we can call Fa1 the second order force ′′ rotating in crank direction and Fa2 the second order forces rotating in the opposite crank directions. The system of forces rotating in the crank direc- tion or opposite to it constitutes a constant rigid system. We can consider the balance of the rigid system of forces in any time instant. Once we have determined the resultant of the system of forces for an instant, in the follow- ing instants the amplitude of the resultant will be the same and the vector will rotate with 2ω. 34 Figure 3.9: Balancing of second order inertial forces General considerations Notice how the horizontal component of the two counter-rotating forces will always cancel out and the resultant will always be obtained by summing the vertical components. The first order forces have a period of 2π while the second order ones have a period of π. The overall inertial force acting on a cylinder is the vectorial sum of rotating and oscillating inertial forces of at least first and second order (possibly also higher orders). The resultant inertial forces are not cancelled out in a single cylinder. In order to balance them, we can use two masses, one rotating with ω and the other rotating with −ω (this way we balance the first order ones). Multi-cylinder engine We can balance the inertial forces in a multi-cylinder engine as we did for centrifugal forces, with the addition of two counter-rotating shafts. In fact, the resultant of the first order forces is zero, since they depend from θ as the centrifugal forces do. Instead second order forces depend from 2θ, so they will all have the same direction, therefore summing up with each other. By adopting a symmetrical lengthwise layout (i even) we can cancel the resultant moment but the resultant force will still be there. In order to balance these second order forces, we use two shaft which rotate with 2ω and −2ω. These shafts have an off-centre mass on them which are located in a normal plane passing through the centre line. The mass can be determined by determining the resultant force RF ′′ (same for the counter- a1 rotating forces). The balanced shaft is called the Lanchester shaft. ′′ RF ′′ = 4Fa1 = 4 · 21 ma ω 2 rλ, to be balanced by mc (2ω 2 )Rx. In the slides a1 35 (PSAV03, 61-68) there are several examples of balancing. 3.4.4 Counterweights in cranks The engine crankshaft has counterweights. In an i-cylinder engine, there are i + 1 main bearing caps for support. The counterweights are needed for reducing the stresses on the supports. We need to make sure that the counterweights produce a balanced field of forces. 3.4.5 Centrifugal and inertia forces, two-stroke engine In two-stroke engines, we can adopt the same lengthwise layout of cranks that we used for four-strokes. If i is odd, we will use the anti-metric length- wise layout (complete balance is not possible) while if i is even, we will have two situations: i 2 is odd: the moment’s resultant is zero; i 2 is even: the complete balance is not possible. In the slides (PSAV3, 71-77) there are several examples of two-stroke engine balancing. 3.5 Balancing of V-engines Before defining what a V-engine is, we need to define two parts of the engine: bank of cylinders: it is a group of cylinders located on the same side of the shaft with their axes in a plane passing through the crankshaft axis; row of cylinders: it is a group of radial cylinders in a plane at right angles to the crankshaft axis and operating on a single crank. Now we can define the V-engine as an engine with two banks of cylinders, with corresponding cylinders in each bank forming a two-cylinder row. The angle between the cylinder planes is called V-angle. Other engines can be the W-engine, which is a V-engine with three banks (the two V-angles are usually equal). We can also have an opposed engine, which is a V-engine with a 180◦ V-angle. Notice that in a V-engine, we have two connecting rods for each crank pin. If the cylinders form a proper V as well, the engine is called proper V-engine. 36 Figure 3.10: Examples of V-engines 3.5.1 Partial rotation principle In order to obtain a V-engine and to maintain the uniform firing of the cycles, we apply the partial rotation principle to the in-line layout. The partial rotation principle states that ”if we rotate the cylinder and the crank rigidly, the phase of the cycle does not change compared to the other cylinders”. There can be several possible layouts for a V-engine and they depend from considerations linked to inertial and centrifugal forces. The partial rotation does not change the time instant in which we have, for example the TDC of combustion. It only changes the spatial position of the cylinder. In Figure 3.10 we can find some examples of V-engines. 3.5.2 Balancing of proper V-engines In many V-engines, the forces due to inertial and centrifugal forces are bal- anced for each bank of cylinders. There are some cases in which the balance of the engine is excellent even tough the banks are not balanced themselves. In general, the best way to analyze the inertial forces in V-engines is to consider a row of two cylinders that acts on a crank. We can project the forces acting on the pistons on the symmetry axis of the row and on the axis perpendicular to it, in order to find the resultant force acting on the row. If Φ is the V angle, and the crank angle for the left cylinder is θ, the crank angle of the right cylinder will be 2π − (Φ − θ) or just Φ − θ if we refer to the crank itself and the direction of the pistons. Both the centrifugal forces and the first order inertial forces that rotate in crank direction are added up and are parallel with the direction of the crank. The contra-rotating first order forces are phase shifted from the other of an angle ψ = 2θ + 2(Ψ − θ) = 2Ψ. 37 (a) First order forces (b) Second order forces Figure 3.11: First and second order forces in a row The second order inertial forces that are still rotating in the crank direction are phase shifted of an angle ψ = 2(Φ − θ) − (Φ − 2θ) = Ψ, while the second order contra-rotating forces are phase shifted from one another of an angle ψ = 2θ + Ψ + 2(Ψ − θ) = 3Ψ. Depending on the V-angle the forces will either cancel each other out or they will be added together. 38 Models of engine processes The main goal of this chapter is to study the main processes that happen inside of the ICE, especially in terms of fuel conversion efficiency. As we de- Wb scribed in previous chapters, the fuel conversion efficiency is: ηf = mf Q LHV. It is convenient to split this efficiency in different components and to analyze each component individually: Wa−f Wi Wb ηf = · · = ηa−f ηθi ηm mf QLHV Wa−f Wi The efficiencies are respectively: the air-fuel efficiency (takes into account the losses due to the fact that the fluid is real), the internal thermodynamic efficiency (takes into account the losses during the process) and the mechan- ical efficiency (takes into account the losses when we transfer the work from the piston to the shaft). We can also consider an ideal efficiency, linked to and ideal work, which is the efficiency of a cycle with an ideal fluid. During our analysis we will consider three types of cycle: Ideal cycle: no losses, we use an ideal fluid; Air-fuel cycle: we have only the losses due to the fact that the fluid is now considered a real fluid; Indicated cycle: we have a real fluid and all of the losses that happen in reality. 4.1 Ideal heat cycle The ideal heat cycle is the simplest way to describe (approximately) the functioning of an ICE. In fact, we have an ideal fluid, which never changes (so the cycle is closed) and never alters its properties and chemical composition. The combustion is modeled as an heat addition to the gas. The ideal gas can be described with the ideal gas law: pv = RT. The constant R is R= R Mmol. Since the gas is ideal, we consider constant cp and cv. As usual, univ c cp − cv = R and γ = cvp is the isentropic coefficient. During our cycle we will have a quantity of heat that is received qin at high temperature and a quantity that is rejected qout at low temperature. 39 4.1.1 Types of cycles We will consider three main cycles, which are all made out of: 1 −→ 2: isentropic compression starting from ambient pressure; 2 −→ 3: combustion (heat received, qin ); 3 −→ 4: isentropic expansion; 4 −→ 1: heat rejection (heat rejected, qout. Notice that the ideal heat rejection phase corresponds to both intake and exhaust phases. In fact the heat addition is actually due to the combustion and the rejection of heat is there in order to account for the spent (hot) charge being replaced with a fresh one. We can model the heat addition as Qin = mf qin = mf QLHV. The term mf QLHV is the energy content of the fuel that we can use during combustion in the real cycle. We can define an ideal efficiency: ηid = wqin id = qinq−q in out = 1 − qqout in. The three cycles that we will consider differ in the type of combustion phase: Otto cycle: the combustion is isocoric and instantaneous; Diesel cycle: the combustion is isobaric. Used for big, slow Diesel engines; Sabathè cycle: the combustion is a combination of an isocoric and of an isobaric transformation. Used in smaller, faster Diesel engines (automotive applications. Regarding the isentropic expansion, we would like to prolong it until a point from which we could have a isothermal rejection phase, since this would greatly increase the work and the efficiency of the cycle. The problem is that the cycle would take too long (the frequency of the cycle would approach zero). Another solution could be to have the expansion end in a point from which we could have a rejection phase that is a constant pressure one. This can be done, but for most cases this is not really a good solution, since the displacement of the cylinder would be too large (see PSAV04 10). Lastly, if we consider the fact that in an engine we have an exhaust and intake phase, we have to add two ”phases” that take these things into account. These phases, tough, happen at the same pressure, so they do not contribute to work production. For each cycle the combustion is complete. 4.1.2 Comparison between cycles We can compare different cycles in terms of efficiency, work and pressure allowed. There are many relationships that we can write for each cycles (PSAV04 18-27). 40 Figure 4.1: Ideal cycles in pV and TS charts Otto cycle We can consider the Otto cycle (very high pressures can be reached after combustion). Its efficiency can be written as a function of the com- 1 pression ratio: ηid = 1 − γ−1. It rc is interesting to see how the effi- ciency changes with respect to the composition of the charge and with respect to the compression ratio. As we move from air to mixtures of air and fuel we can notice a change in γ, which affects the efficiency (low- ers it). The compression ratio is also a factor. When it increases, the ef- ficiency increases as well. We can notice that for larger compression ratios we have an increase of effi- ciency that is not that great. We can also say that increasing γ at constant rc leads to an increase of Figure 4.2: Efficiency for an Otto cy- maximum pressure, which increases cle the work. We need to make sure that the maximum pressure (p3 ) is not too large, otherwise we will risk to damage the engine. At least we will need a larger and stronger engine. In fact, we would like to have an high imep p3 ratio. 41 Figure 4.3: Comparison between cycles Diesel and Sabathè cycles ′ 1 τ γ −1 We can write the ideal efficiency of Diesel cycle as ηid = 1 − γ(τ ′ −1). rcγ−1 ′ T3b τ = 3a. Comparison of the cycles As we can see from Figure 4.3, we have very different maximum pressures between Otto cycle and the other two. The higher maximum pressure makes the Otto cycle the best in terms of work and efficiency. This can be said by fixing the fluid, the compression ratio and the energy inserted in the cycle. Like we said before, having a too high maximum pressure can be dangerous for the engine. In particular, for SI engines, a too high p2 can lead to self- ignition, which generates the knock phenomenon. This is why we usually use Otto cycles for SI engines, since we can limit p2 and have a larger p3 and a large work and efficiency. On the other hand, for CI engines, we do not care about the value of p2 , since we do not have fuel mixed with air during the compression phase. So we usually use Diesel (or Sabathè) cycles for CI engines. The limitation is on p3 , in order to avoid engine damage. We can see from Figure 4.4a, the Otto cycle is the best when we have a fixed rc and no restriction on the maximum pressure. Instead, from Figure 4.4b we can see that the Diesel cycle is the best when the maximum pressure is fixed. Notice how, in this 42 (a) Fixed rc (b) Fixed pmax Figure 4.4: Comparison in different conditions case, we need to have a lower p2 in the Otto cycle in order not to go above the maximum pressure p3. Notice how we also fixed qin for both cases. Similar considerations can be made by fixing qout (PSAV04 32). 4.1.3 Over-expanded cycles Like we were saying before, we would like to keep the expansion going until a point from which we can then have the heat rejection phase at a con- stant pressure. We also said that in order to implement this solution,we would need an larger engine displacement. Some engineers have actually devised two solutions for this problem. These two were Atkinson and Miller. Atkinson’s engine idea is very complex and we will not consider it in this notes. Instead, Miller’s engine is much simpler and achieves this over-expansion in a very interesting way. Basically we tweak the intake valve opening timing in two ways: either we close it early (early intake valve clos- ing EIVC) or we close it late (late intake valve closing LIVC) with respect to the BDC position of the piston during intake. As we can see from efficiency and impep ratios with the Otto cycle, the Miller cycle can be a valid alter- native. We use Miller’s cycle in large Diesel engines for ships, but also for some niche automotive applications (Mazda Millenia). From the expression of Miller’s cycle efficiency (PSAV04 38) we can see that it is the only cycle which depends from qin in the efficiency expression. Early intake valve closing In this case, we have that we open the valve at the end of the expansion, but we close it before the piston reaches the BDC. This means that the gas 43 (a) EIVC (b) LIVC Figure 4.5: Comparison in different conditions will be expanded first, as the piston keeps moving downwards (point 7 in Figure 4.5a and then it will be compressed back at the pressure with which it entered the cylinder (point 1) and it will start the compression phase. We obviously have less charge in the cylinder than we would have in a regular Otto cycle. This affects the work, diminishing it but it increases the cycle’s efficiency. Late intake valve closing In this case (Figure 4.5b) we close the intake valve after the piston has reached BDC (normally we would close it at point 5, but we close it at 1). this means that some charge will actually be pushed back inside of the intake manifold. This means that we will have less charge inside of the cylinder, again reducing the work. The efficiency is actually improved. 4.2 Air-fuel cycles Up until now we have considered ideal cycles, in which the charge never changes composition ad it is never replaced (we add some extra strokes to represent its replacement). In the so called air-fuel cycles, we add this phe- nomenon: the gasses change chemical composition during the combustion phase. We will not consider any other loss that is not related to the fuel burning in a ”real” way. The composition of the working fluid changes during the cycle. During in- take and compression, the mixture of air (N2 + O2 +...) and fuel (in vapor form) can be considered frozen, since it does not alter its properties that much. For CI engines, the charge is just air plus some remaining burned 44 (a) Miller/Otto efficiency ratios (b) Miller/Otto imep ratios Figure 4.6: Efficiency and imep ratios gasses. When air and fuel react chemically during the combustion, an equilibrium condition might be reached in which we not only have the products of the combustion, but also some of the original reactants that were obtained by recombination of the products at high temperature (T > 1850K). This phe- nomenon is called dissociation and it is an unwanted phenomenon since it takes some useful heat away in order to recombine the products into the re- actants. As the combustion products cool down, another phenomenon called recombination happens, but it cannot compensate for all of the power lost because of dissociation. During exhaust, we can consider the gas composition as frozen again. The fluid properties are no longer constant (when the mixture is not frozen) and are depending from the temperature (cp (T ), cv (T ) −→ γ(T ). 4.2.1 Cycle description As we can see in Figure 4.7 we can see some examples of air-fuel cycles which differ from one another in the way in which intake and exhaust take place. The compression is a reversible adiabatic, the combustion is complete with no heat loss, the expansion is a reversible adiabatic and the exhaust/intake are considered ideal. Usually the power in a SI engine is controlled by controlling the pressure in the inlet manifold. If the pressure is less than the environment one, the engine is said to be throttled, while if the pressure is more or less the atmospheric one, the engine is unthrottled. If the inlet pressure is higher than the atmospheric one, the engine is supercharged. 45 Figure 4.7: Air-fuel cycles Ideal exhaust and intake As we said before, the intake and exhaust phases are considered as ideal. We will have adiabatic reversible processes, valve events will occur instantaneously at TDC and BDC, with no change in cylinder volume while the pressure difference across the valve falls to zero. In the un- trhottled cycle, we have an isocoric fall of the pressure to environment pressure. The remaining gasses fol- low the transformation (4 −→ 5). If the external pressure is not equal the one in the cylinder, we will have some fresh charge or some burned gas flowing into the intake mani- fold until the pressure is equalized. Since there is no heat transfer, the residual fraction of spent gasses is fixed, because the state of the re- maining gas at point 6 (Figure 4.8) Figure 4.8: Detail of intake/exhaust is the same of the state at point 5, at the end of the isentropic expansion of the gasses in the cylinder at the exhaust pressure. 46 Figure 4.9: Comparison with an ideal cycle 4.2.2 Air-fuel cycle efficiency As we said at the beginning of this chapter, the efficiency of the air-fuel cycle is defined as: Wa−f ηa−f = mf QLHV This efficiency is affected by a few factors: dependence of the specific heats from the temperatures (PSAV04 55); dissociation; variation of the specific gas constant before and after combustion be- cause of a variation of number of moles and of molar mass (usually R increases). We can see from Figure 4.9 the real and air-fuel cycles are the same during compression but start to differ greatly during combustion and expansion. The efficiency is obviously lower. 4.2.3 Dissociation Definition of the subtangent of a thermodynamic transformation We can define a useful concept called subtangent of a thermodynamic transformation. We can start from a point A and trace a line tangent to the transformation line in point P. We can write: T dS = dQ + dWw = cdT dT T = dS c 47 Figure 4.10: Subtangent of a thermodynamic transormation dT T = tan ϕ = dS AB We can say that AB = c is the subtangent of the polytropic curve in P. If the point was somewhere else, we would have a different tangent line but the same subtangent. Dissociation (a) Effect of dissociation (b) Quantity of dissociation Figure 4.11: Dissociation 48 The dissociation of products into reactants can occur at temperatures higher than 1850K and if the mixture is in the right proportions of air and fuel. Usually dissociation does not occur in lean mixtures, since the temper- ature reached is not high enough. It also does not occur in rich mixtures, since the presence of CO in the burnt gasses (rich mixtures have a great quantity of CO) suppresses the dissociation of CO2. The phenomenon of dissociation is most evident in mixtures which have stoichiometric propor- tions. We can define a mixture richness through the degree of richness: degr = φ − 1, where φ = 1/λ. 4.2.4 Air-fuel cycle analysis The first part of the analysis concerns the variation of the specific gas con- stant. In fact, due to the fact that the number of molecules changes espe- cially during combustion, the constant R is modified as well. Actually, this is a phenomenon that benefits the efficiency of the air-fuel cycle, since the ′ constant is reduced and pp23 = RR TT32 means that for the same p2 , the maxi- mum pressure achievable in the air-fuel cycle is greater than the one for the ideal one, meaning a larger cycle area and a larger work. Summary The overall efficiency of the air-fuel cycle is smaller than the one of the ideal cycle. The variation of the specific heats and the dissociation process contribute to the lowering of efficiency. The variation of R slightly increases the efficiency of the air-fuel cycle, but it is not enough to win over the other two phenomena. Influence of the air-fuel ratio The air to fuel ratio determines the temperature T3 at the end of com- bustion and therefore influences the fuel-air efficiency. In a lean mix- ture, we will have lower tempera- tures because of the dilution of the fuel in a greater mass of air. This means that the phenomena related to large temperature variations like specific heat change and dissocia- tion, will be lower. This means that with an increase in α, we will have a slight increase in efficiency. For a rich mixture, instead, we will have higher temperatures, so we will see Figure 4.12: Effect of α 49 phenomena like the dissociation be- ing very present. So, smaller values of α lead to smaller values of effi- ciency. Also, the fuel that is not oxidized is ”wasted”, meaning that we do not use its energy. We can see the influence of α in a graph. 50 Real engine cycles In this comparison of a real engine cycle with the ideal and air-fuel ones we will consider a spark ignition engine. Similar considerations can be done for the compression ignition engine. In Figure 5.1, we can see the graphical comparison of a real cycle with an air-fuel one. The value that takes into account the losses due to ther- mal effects is the thermodynamic efficiency (which is not a concept that is present in the Anglo-Saxon literature): Wi ηθ,i = Wa−f Notice that geometrical parame- ters like the compression ratio and chemical parameters like the com- position of the fuel are the same for both cycles. In this chapter we will analyze what is different between Figure 5.1: Graphic comparison be- the two cycles, that is the thermo- tween cycles dynamic losses. These losses are five and they will be analyzed one by one in order of importance. The losses reduce the work of the cycle (of a finely tuned engine) to about 85% of the equivalent air-fuel cycle. 5.1 Heat transfer The most important cause of losses is the heat transfer from the charge to the cylinder walls. This loss cannot be avoided (the temperatures can go as high as 2500K in the cylinder) but can be at least addressed and hopefully minimized. We can define the heat flux as Q̇ = h(Tg − Tw )A [W], or, for the specific quantity q̇ = Q̇ 2 A = h(T − g − Tw ) [W/m ]. The parameter h is the heat transfer coefficient from charge to wall and varies with the geometry. During combustion and expansion the heat goes from gas to cylinder, while during compression the flux goes from cylinder to 51 gas. In order to avoid cracking of the engine and of the cylinder walls (and also improper work of the components like the spark) we need to provide adequate cooling (T < 400◦ C for cast iron and T < 300◦ C for aluminum alloys). 5.1.1 Effects of heat transfer Heat transfer has many negative effects on the engine performance. It re- duces the average temperature of gasses at combustion, thus lowering the work per cycle transferred to the piston (lower maximum pressures). In addition to that, knock could be more present, because of the heat coming from the cylinder walls, exhaust valve and piston to the gas in the compres- sion phase. In order to avoid the onset of knock, we need to further reduce the compression ratio, thus reducing our output power and efficiency. Other negative effects concern the exhaust gasses. In fact, the lower exhaust gas temperature reduces the the possibility of afterburning of CO and unburned hydrocarbons at the exhaust. This increases the engine emissions to the emission after-treatment devices. Temperature of the exhaust gasses can also affect the power that can be obtained from devices like turbochargers. The volumetric efficiency λv is also reduced, since we have a lower air den- sity in the cylinder (lower mass). Lubrication and friction are two other parameters that are affected by the heat transfer. From Figure 5.2, we can see what is the effect of heat transfer in a T-S chart. We can see that in the combustion phase the gas is receiving heat from the walls (increase in entropy) until the com- pression reaches a point in which the temperature of the fluid is larger than the one of the walls. Since the temperature T2′ is smaller than the T2 of the air-fuel cycle, we will also have a maximum temperature that is lower as well. This obviously af- fects the work. In the expansion phase we can see that the entropy decreases, which means that the gas Figure 5.2: Effect of heat transfer is giving heat to the walls. We can clearly see the portion of area that we are no longer using (work lost). The heat transfer rate decreases during expansion because the gas temperature is becoming lower. We can define the fraction of burned mass as xb = mmtot b and follow the combustion considering this parameter. 52 Figure 5.3: Effect of finite combustion Timing of the heat transfer The importance of the moment in which the heat transfer occurs is very important. In fact, if the heat transfer happens after combustion, we will loose precious work because of the lower pressure that will be reached. If instead we have heat transfer at the end of expansion, we will not loose much work, since the spent charge would be expelled anyway and the heat of those gasses lost. 5.2 Finite combustion time In real cycles the combustion is not instantaneous. This means that while it happens, the piston is moving. In ideal cycles we used to initiate the combustion (via the spark plug) at TDC, thus achieving the maximum work. If we did that in reality, we would have the combustion starting after the piston reaches TDC, during the expansion stroke. This would limit the brake work and increase the temperature of the exhaust gasses. This is why we initiate the combustion before TDC. We can notice from Figure 5.3 that the maximum pressure reached will be lower since the combustion occurs and ends after TDC, when the volume is larger. The pressure during the expansion tough, is larger, since we are having combustion. 5.2.1 Spark timing and spark advance In order to maximize the work,the spark has to be released at the appro- priate time during the compression stroke. Even tough we want to achieve maximum torque, we sometimes need to time the spark emission in order to reduce emissions or knock. Unfortunately, there is no rule that works for all engines when it comes to deciding when to ignite the mixture. Usually timing is found by means of experimentation. Modern engines can change the spark timing depending on the operating conditions. The crank an- gle, calculated from TDC, at which we ignite the mixture is called spark 53 (a) Spark advance vs pressure (b) Spark advance vs relative torque Figure 5.4: Effect of spark advance advance. We can clearly see from Figure 5.4a that the higher the spark advance, the higher the maximum pressure that we get. This is limited by the fact that we must not have combustion before TDC or we will get neg- ative torque. Usually, tough, the maximum torque is found at lower spark advance angles. SA is also limited by the onset of knock or by the need to have a slightly higher exhaust gas temperature to favour post-oxidation of CO and hydrocarbons. The usual spark advance lies between 40◦ and 10◦ before TDC. We can make similar considerations for compression ignition engines, sub- stituting the spark with the injection of fuel. Combustion usually starts shortly before TDC, with peak pressures reached between 5◦ to 10◦ after TDC. 5.3 Exhaust blowdown losses In a real engine cycle the exhaust valve is opened before reaching BDC in order to reduce the pressure during the first part of the exhaust stroke. Basically we trade some expansion stroke work in order to reduce the the pumping work afterwards. This will increase the net work. Usually the valve is opened about 50◦ before BDC (PSAV05 26-27). 5.4 Crevice effect and leakage The engine combustion chamber is connected to several small volumes called crevices, because of their narrow entrances. Gas can flow into these volumes 54 during the operating cycle. The largest crevices are the volumes between the piston, piston rings and cylinder wall. Some gas can even escape these regions and flow into the crankcase. This gas is called blow-by gas. If the gas that flows in the crevices is a mixture of air and fuel, it will not burn and will be wasted. Fortunately, most of this gas will return to the chamber and be burned in the following cycle. In a well designed engine, leaks of this kind are very small. They, however, reduce the pressure during compression, combustion and during expansion. Leakages depend from the cross-section passage in pressure between the two connected regions. This phenomenon will decrease as the engine speed increases. In order to compensate for blow-by, we have pipes that bring these escaped gasses back into the chamber. 5.5 Incomplete combustion If the combusti

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