Real Engine Cycles PDF

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...

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 e↵ects is the thermodynamic efficiency (which is not a concept that is present in the Anglo-Saxon literature): Wi ⌘✓,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 di↵erent 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 A = h(T g Tw ) [W/m2 ]. 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 E↵ects of heat transfer Heat transfer has many negative e↵ects 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 e↵ects 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 a↵ect the power that can be obtained from devices like turbochargers. The volumetric efficiency v 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 a↵ected by the heat transfer. From Figure 5.2, we can see what is the e↵ect 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 T20 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: E↵ect 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: E↵ect 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: E↵ect 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 e↵ect 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 combustion is not complete, exhaust gasses will contain combustible species. this means that the chemical energy released inside the engine is lower than the one introduced in the cylinder (about 5% lower). This phenomenon is particularly evident for rich mixtures, in which there is not enough oxygen with respect to the fuel in order to complete combustion. We can compute a combustion efficiency (PSAV05 24) by considering the burned mass with respect to the total one. In Diesel engines this ef- fect is usually smaller, with a combustion inefficiency lower than 0.02. At higher speeds we can mix the charge better, thus increasing the percentage of burned fuel. 5.6 Considerations on heat transfer We can perform a heat release analysis in order to estimate how the chemical energy of the fuel is released. We usually neglect the heat transfer for simplicity (we have a net release). We can see that the pressure signal provides a lower energy with respect to the fuel chemical energy. 5.6.1 Engine energy balance We can compute an overall energy balance of the engine: ˙ + Q˙oil + Qmisc ṁf QLHV = Pb + Qcool ˙ + He,ic ˙ + Ḣe the last two terms are the exhaust enthalpy due to incomplete combus- tion and the exhaust enthalpy due to high temperature of exhaust gasses. Usually Pb is only (38 ÷ 42)% of the power introduced for SI and around (44 ÷ 50)% for CI. The energy balance of an engine is very complicated. 55 In Figure 5.5 we can find the con- tribution of all parameters with re- spect to the load. We can also deter- mine where the heat taken away by the cooling system comes from. We have heat transferred to the walls from the gasses, heat transferred to the exhaust port and valve, a substantial fraction of the friction work (piston-walls, etc.) and heat transferred to the lubricant oil if an oil-to-coolant heat exchanger is em- ployed. In the slides (PSAV05 44- 49) we can find the evaluation of all heat terms and enthalpy terms. Since some of these quantities de- pend on QLHV , they will change de- Figure 5.5: Engine energy balance pending on the fuel used and so, on with respect to load the engine type. 5.6.2 E↵ect of combustion chamber shape on heat transfer Supposing the piston fixed at TDC during the whole combustion process, the shape that has the least surface for the heat transfer is the sphere. This solution, tough, is not adopted, since the piston stroke would have to be extremely large. In addition to that, there would be excessive thermal stresses and a thin zone in which there would be unburned gasses. This is why the most adopted shape is the cylindrical one. The least surface is obtained for the so called square cylinder, which is a cylinder of height equal to the bore. We can also define the stroke to bore ratio ⌫ both at TDC and BDC (PSAV05 54). We can have three configurations of cylinders depending on ⌫: ⌫ = 1 (B=S): square engine; ⌫ < 1 (B>S): over square engine (or short-stroke); ⌫ > 1 (B 1 (which is also the best condition for heat transfer). For SI engines, instead, we have ⌫ slightly lower than one since we need to reduce the mean piston speed: u = 2Sn with n in rps. We want to reduce u because pressure drops (losses) are dependant on the square of the fluid velocity (in turbulent conditions). The 56 fluid velocity depends on u2 , so, in order to reduce them, we need to reduce u. Since u depends from S and n, we need to reduce the stroke instead of the engine speed because the overall power and torque depend on it. For Diesel engines we have that the speed is already lower with respect to SI engines, so the problem is not present and we can have ⌫ > 1. 5.6.3 Heat transfer between burned gas and cylinder walls As we said at the beginning of the chapter, we can write the heat transferred as Q̇ = h(Tg Tw )A. We can actually consider the mean temperature di↵erence between gas and wall, so Q̇ = hA Tm. In order to be able to compare di↵erent engine performances with respect to their heat transfers, we can divide the heat transferred by the energy flow rate introduced with the fuel: Q̇ ṁf QLHV It can be demonstrated (by simple calculations and substitutions that are in PSAV05 55) that Q̇ h Tm ↵ / ṁf QLHV ⇢i u For SI engines, the air-fuel ratio is basically constant and also the average temperature is constant. This means that Q̇ h / ṁf ⇢i u We have many estimations of h the most famous of which being the Woschi’s correlation, which states that h = CB 0.2 p0.8 T 0.8 w0.8. This correlation can be simplified as h / (⇢i u)0.8. So we can say that Q̇ 1 / ṁf (⇢i u)0.2 For CI engines, the volumetric efficiency is constant as well as the intake air density. we can then say that Q̇ h Tm ↵ Tm ↵ / / ṁf u u0.2 In general, (PSAV05 58-59 for graphs) heat transfer is the highest at low speed and high load. 57 Mechanical efficiency In previous chapters the mechanical efficiency was briefly defined. Now we will take a closer look at what the mechanical efficiency represents. It is defined as the ratio of the brake power delivered by the engine and the indicated gross power: Pb Pf ⌘m = =1 Pig Pig The term Pf is the friction power, which comes from the friction work, which comprises many phenomena that cause losses (maybe not even due to friction). This work can be as large as 100% of the engine delivered power (idle condition). Often the distinction between a good and a bad engine is made by the frictional losses. Most of the friction losses is in the form of thermal losses that are sent to the coolant and the lubricating oil. These thermal losses are then dissipated in the oil cooling system and in the radiator. We will define three losses which will be grouped in the total friction losses (friction losses for simplicity). We need to spend power in order to: overcome the resistance to relative motion of all moving parts of the engine (mechanical friction work). Examples are friction between piston rings, piston skirt and cylinder wall, friction in the wrist pin,... drive engine accessories (accessory work), which are the mechanisms essential to the engine functioning plus the ones that are anyway di- rectly powered by the engine. This includes the water pump, the oil pump, the fuel pump, the compressor of the AC system,... draw fresh mixture through the intake system into the cylinder and to expel gasses from the cylinder (pumping work). This work is only defined for four-stroke engines. The total friction work is the sum of those three works and can also be computed as Ptf = Pig Pb. 6.1 Pumping work The pumping work changes depending on whether we are talking about a naturally aspirated engine or a turbocharged one. In naturally aspirated engines we have that the intake pressure is lower than the atmospheric one 58  (a) Pumping work NA engine (b) Pumping work SC engine Figure 6.1: Comparison between NA and SC engines due to flow resistance so the pumping work will be negative (we need to do work in order to induce air in the cylinder) and will take a part of the gross indicated work. The throttle valve position influences the pumping work (it is lower when we are at full throttle). For turbocharged engines, instead, we have flow resistance, but the intake process is governed by the turbocharger’s compressor and turbine and therefore the work might be positive. In Diesel engines we have an exhaust gas temperature which is lower than the one of the SI engine’s one. This means that we will have a much lower (positive) pumping work. For most engines we need to respect regulations on the N Ox emissions. This is why we implement an EGR system at high pressure in order to recirculate part of the exhaust gasses back into the intake manifold. The problem is that this recirculation works because of a pressure di↵erence between exhaust port and intake manifold. This imposes that the pumping work has to be negative. For supercharged engines (mechanical compressor driven by the engine) we have no back-pressure due to the presence of the turbine, so we can have a positive contribution of the pumping work. 6.2 Measuring friction We can see that the friction work depends both on the speed and on the load (bmep). It is generally average for low speeds and low loads, pretty low for low speeds and high loads and very high for high speeds and average loads. We can notice that the friction changes with the load but always increases when we increase the speed. The crank mechanism and piston assembly are the main sources of friction work. We can take a naturally 59 aspirated gasoline SI engine as an example. We have: (10 ÷ 15)% of friction work done by the crankshaft, (25 ÷ 30)% done by the piston and conrod, (10 ÷ 15)% done by the auxiliaries, (10 ÷ 15)% done by the valvetrain and (30 ÷ 45)% pumping work. In small turbocharged Diesel engines, we have a much smaller pumping work and the component due to pistons and conrods is significantly higher due to higher pressures. 6.2.1 Mean e↵ective pressures We can analyze the e↵ect of friction by considering the meps relative to each work. We can recall that the mep is defined as W mep = Vd We can define the amep, mfmep, pmep and the mep relative to the to- tal friction work: tfmep. The relationships between the meps reflect the relationships with works: tf mep = amep + mf mep + pmep and bmep = imepg tf mep. For turbocharged engines we can neglect the contribution of pmep. 6.2.2 Friction measurements methods In this section we will analyze the main methods used to measure the friction inside of an engine from most precise to most approximate. Indicator diagram method This is the only method that can compute the friction inside of the engine in a direct way. We basically measure the imepg and the bmep and we compute the tfmep by subtracting the two of them. We need a pressure transducer for each cylinder and a crank angle sensor, in order to obtain a pV diagram from the p✓ diagram. This allows us to compute the mep at the piston and the mep that we get at the crank. From these two values we can see how much we are loosing. Direct motoring tests Another less precise method is the direct motoring method. We basically connect the engine to an electric motor which moves it. The engine is not having cylinders firing. We know the torque that we are giving the engine and that is the torque needed to overcome friction. If we fire the cylinders we can also compute the bmep. Notice that friction in firing and in motoring can be di↵erent. Temperatures are lower in motoring operations which means that the oil viscosity might be greater, thus increasing the viscous friction. In addition to that, piston-cylinder clearances are greater 60  Figure 6.2: Willans lines in motoring operations, which tends to make the friction lower. In motoring, we only have the compression pressure on the piston and not the pressure of the firing cylinders. We have no exhaust phase and gasses discharged have an higher density than the ones in firing condition. When motoring, the net work is done in the compression and in the expansion phase. Willans lines These lines are extrapolated from operating points in a fuel consumption bmep chart. Basically, we extrapolate the lines until zero fuel consumption. The values of bmep which are negative are the values of fmep. Morse test In a multi-cylinder engine, a single cylinder is stopped from firing. This creates a reduction of brake torque while the friction losses are still present at maximum level. We need to make sure that cutting out one cylinder does not significantly a↵ect the functioning of the engine. Free deceleration curves We obtain speed versus time curves by decelerating the engine without a load or without firing. Knowing the inertial moment, the tangent to the deceleration curve allows the total torque loss for every speed case of interest to be calculated. 61 6.3 Total friction work We have several types of friction work that we can have. One is the one that is done by the pressure forces acting on the piston and in the cylinder. They depend from the engine load. We then have friction work done by inertia forces. Finally, we have the forces that generate various friction works (valvetrain,...). 6.3.1 Piston assembly friction A great cause of friction is situated at the piston assembly. We have that the piston skirt (which is a load bearing surface which keeps the piston aligned with the cylinder bore) is loaded by the side loads which are present when the connecting rod is at an angle with the cylinder axis. We can make a balance of the forces acting on the piston and connecting rod by considering also the side forces. Whenever the conrod has an angle with the cylinder axis, a thrust force will be generated, which in turn generates a friction force on the sides of the cylinder. We can compute the forces due to the gas pressure and put them in relation with the ones that are lateral loads. The vector sum of these lateral and axial forces is the force that we see on the conrod’s axis (PSAV06 24-30 for calculations). The thrust force is transmitted to the liner via the rings and piston skirt. It changes direction as the piston passes through TDC and BDC positions. The friction changes sign at these locations and the gas pressure during expansion is greater than the one in compression, we can say that the friction forces is larger in expansion than in compression. The side of the liner resisting that greater force is the major thrust side, while the other side is the minor thrust side. Friction work of in-cylinder gas pressure forces can be modeled as WfI = KI Vd pmax 6.3.2 Friction work of inertial forces We also have inertial and centrifugal forces acting on the piston. These forces give rise to a certain amount of friction forces on the sides of the piston and cylinder. In the slides all calculations are performed (PSAV06 31-34 also for other considerations). Inertial forces work can be defined as WfII = KII ma u2 6.3.3 Friction work of generic friction and accessory work This work is independent from all forces that we have previously examined. Generic friction includes by the ring tension that acts to force the ring against the liner. Valve train friction is another part of this generic friction. 62 We also have the work needed to make the pumps function, AC compressor functioning,... Usually we can use chain drives from the engine to these accessories. Usually we do not include the work used for fans, generator and power-steering pump. Obviously a fully equipped engine delivers less power since it has more accessories. The amep can be represented as a second order polynomial function, as a function of the speed. We can write the generic friction work and the accessory work as functions of the displacement as WfIII = KIII Vd Pumping work and pumping friction As we said before, the pressure inside of the cylinder at intake is lower than the ambient one because of the resistance of the fluid in each part of the intake manifold. The total pressure drop is the sum of all of the losses inside of the intake system: air filter, throttle valve, inlet manifold, inlet port and inlet valve. Port and valve contribute to the largest losses. The pressure at exhaust is higher than the environment one and the pressure drop be- tween cylinder and environment is due to the exhaust manifold, and tailpipe, catalytic converter and mu✏er. The pumping work per cycle is the inte- gral of the pressure over the volume over the inlet and exhaust strokes. The work Vd (pim pem ) is the work due to the e↵ect of restrictions out- side the cylinder in the inlet and outlet system and it is called throt- tling work. The other area in Fig- ure 6.3 is the valve flow work and corresponds mainly to pressure losses in the inlet and exhaust valves and, to a less extent, in the inlet and exhaust ports. As the load is re- duced (throttle valve not fully open) for SI engines, the throttling work increases and the valve flow work Figure 6.3: Pumping loop diagram decreases. The throttling work in- creases more than the valve flow work decreases. If speed increases, both works will increase. The pumping work can be expressed as Wp = V d ( pi pe ). As a result, the pressure in the cylinder during intake pro- cess can be 10 to 20 percent lower than the atmospheric one (at WOT). We can find a relationship between the pressure drop through the intake valve and the operating parameters of the engine. The process of intake will be studied as a quasi-static process. We can apply the first law of thermody- 63 namics (Eulerian approach) between the points 0 (intake manifold) and i (in the cylinder): Z i Wt = vdp Ek W w = 0 0 with Wt being the technical work done in the manifold and Ek ⇡ 0. We can then write the wasted work as Z i p0 pi Ww = vdp ⇡ 0 ⇢ If we apply a similar approach between 0 and r (inside of the valve) consid- ering the technical work equal to zero and the wasted work equal to zero (as if we were in a converging nozzle) we could get Z r Wt = vdp Ek W w = 0 0 Z r p0 pi Ek = vdp ⇡ 0 ⇢ From this last equivalence we can say that the kinetic energy of the flow will be dissipated between r and i. In particular, it will be dissipated by vortexes. 2 w02 wr2 We can therefore write the pressure drop as | p| = ⇢( w2r 2 ) ⇡ ⇢ 2. In the slides there are other methods to write the pressure di↵erence (PSAV06 44-45). Particularly, the pumping work can be expressed as Wp = KIV pu2 Vd 6.3.4 Total friction work and mechanical efficiency The final expression of total friction can be expressed as the sum of all friction contributions: Wtf = KI Vd pmax + KII ma u2 + KIII Vd + KIV pu2 Vd The mechanical efficiency can be then written as KII ma u2 Ptf tf mep KI Vd pmax + Vd + KIII + KIV pu2 ⌘m = 1 =1 =1 Pig imepg imepg Finally, we can write the mechanical efficiency as a function of the engine 2 speed (with imep constant): ⌘m = 1 A+Bn imep or as a function of the imep C(imep)+D (constant speed): ⌘m = 1 imep. If we suppose C ⇡ const. (no dependence from the imep) we can write the efficiency as an hyperbole: E ⌘m = 1 imep. The mechanical efficiency is zero when we are at idle condition and can be as high as 0.9 (SI engines) at low to mid engine speeds. We have other models for the calculation of the tfmep (like Chen and Flynn method) in which we model the losses as functions of the engine speed in a polynomial expression (PSAV06 52-54). 64 Gas exchange processes In order to replace spent gasses with fresh charge, we need to have some gas exchange processes happening inside of the cylinders. We can see that the brake power depends from the inducted mass of air at fixed air to fuel ratio: ṁa Pb = ⌘f QLHV ↵ Therefore, the main goal of gas exchange processes is the induction (and retaining) of the correct amount of air (the maximum) inside of the cylinder. In fact, the amount of air inducted limits the amount of fuel that can be burned. Another important goal is mixture preparation: we want the air to be properly mixed, in the right proportions. The third goal of these processes is to create the right turbulence inside of the cylinder. The volumetric efficiency can provide an indication on how good the process is: ma ṁa v = = ⇢a Vd ⇢a iVd n/2 We can take as the reference density either the environment air density (NA engines) and evaluate the overall volumetric efficiency or the inlet manifold air density (SC and TC engines) and evaluate only the volumetric efficiency in the inlet manifold, cylinder and inlet valve/port. An high volumetric efficiency is not only achieved through a good design of the processes, but also by a good design of the inlet manifold, valves, etc. 7.1 Airflow and load regulation In SI engines, a requirement for a good combustion is that ↵ is not far from stoichiometric conditions. So, if we want to control the output power (for instance to reduce it) we need to increase or decrease both the mass of fuel and the mass of air in the same proportion. This is why we need a throttle valve. In CI engines, instead, we do not need to control the mass of air, since the fuel does not need to be in strict proportions with the mass of air. We still have a throttle valve in order to improve EGR at low load. In fact at low load, the pressure di↵erence between intake and exhaust is not very large and so gasses are not easily fed back into the inlet manifold. Thanks to the throttle valve we can increase this pressure di↵erence in favour of EGR. In addition to that, the throttle valve is closed when we switch the engine o↵, making sure that we will have a prompt stop of the engine (no air means no combustion). 65 7.2 Intake and exhaust processes in the four-stroke engine In this section we will refer to NA engines. We have that in the intake system there are several pressure losses as the mixture passes through each component of the intake system. We can also say that the induced mass of air is lower than the reference mass. One of the reasons is the presence of burned gasses inside of the combustion chamber at the end of the exhaust process, which have a pressure higher than the atmospheric one. At the beginning of the expansion stroke, the gasses expand, filling part of the displaced volume, which should be filled with fresh gasses (Vi < Vd ). In addition to that, the pressure inside of the cylinder at the end of the induction stroke is lower than the atmospheric one because of the frictional losses along the intake system. This means that the density of the air will be lower than the reference one (hence less mass). In order to have some more air, we will close the inlet valve after BDC, during the compression stroke. Lastly, there is some heat being exchanged between the engine walls and the mixture, increasing its temperature and therefore decreasing its density. 7.3 Phenomena that a↵ect volumetric efficiency The volumetric efficiency is a↵ected by several phenomena that happen in- side and outside of the cylinder. We will discuss all of them in this section. 7.3.1 Quasi-static e↵ects These are the e↵ects that influence the amount of air inducted in the cylin- der. Fuel composition, air/fuel ratio, fuel vaporization, intake air tempera- ture, etc. all belong to these e↵ects. E↵ect of intake and exhaust pressures Let us take an idealized four-stroke induction process for an air-fuel cycle of a naturally aspirated engine. We have that the fresh mixture and the residual gasses are perfect gasses, the inlet pressure and temperature are constant, the exhaust pressure is constant and the valves are opening and closing instantaneously at TDC or BDC. Also, we will not have any heat exchange. We can apply the conservation of mass law, the ideal gas law and the first law of thermodynamics in order to arrive to an expression of the volumetric efficiency that is " pe # pi pi 1 v = 1 (7.1) pa (rc 1) 66  Figure 7.1: E↵ect of gaseous fuels We can notice that pressure drops at the intake are much more detrimental with respect to pressure drops at the exhaust valve. E↵ect of fuel composition, phase and fuel/air ratio In CI engines without EGR, the definition of volumetric efficiency is exactly applied, since only air is induced inside of the cylinder. For SI engines, instead, we have to consider that the composition of the charge is not just made out of air. The fuel can be in two states: liquid state and can be totally or partially vaporized during intake; gaseous state. If the fuel is liquid, we need to distinguish between port (fuel injected in the intake manifold) and direct injection (fuel directly into the engine). In case of port injection, we have some vaporized fuel (and some water vapour) which reduce the partial pressure of the air below the total pressure of the mixture: pi = pa,i + pf,i + pw,i. We can see from Figure 7.1 that fuels which are mostly gaseous have a lower pa,i /pa ratio, thus having a lower volumetric efficiency. Fraction of fuel vaporized and heat of vaporization If the fuel is liquid when it is injected, it might evaporate. The vaporization process takes a certain amount of heat which could be provided by the air, thus reducing its temperature. Usually the later the vaporization happens, the better the volumetric efficiency is. On the other end, tough, the earlier the fuel vaporizes, the better are the mixing process and the cylinder to 67 cylinder distribution. When we have port injection, the fuel impinges on the intake valve and port walls. This means that the thermal energy needed for evaporation is actually provided by the walls rather than from air. If we increase the droplets size, we will evaporate them by using more energy coming from the walls. All of the fuel that is not vaporized in the intake manifold is then vaporized inside of the cylinder thanks to heat transfer from the surrounding air. We can express the ratio of volumetric efficiencies between CI and SI in terms of the fraction of vaporized fuel mass (x): v,SI xrf x ⇡1+ v,CI 2(↵cp + cf )T ↵ where is the ratio between the density of the fuel vapour and the density of air. If we have direct injection, instead, the fuel is fully vaporized inside of the cylinder, meaning that we will have a considerable reduction in air tempera- ture, thus providing a greater volumetric efficiency. In case of gaseous fuels we have that the volumetric efficiency takes the mass of the mixture as a reference: mmix mmix v = = mmix,id ⇢mix Vd E↵ect of ambient conditions The e↵ect of ambient pressure on the volumetric efficiency is not present since if there is a variation in pa , there will be a variation of the same measure on pi (Equation 7.1). The temperature of the ambient should not p influence the volumetric efficiency but experimental tests indicate that v / Ta. We can see that when the external ambient temperature increases, the intake air temperature increases as well. This means that the temperature di↵erence between cylinder walls and charge decreases. This means that we will have a reduced heat transfer to the gasses, increasing the volumetric efficiency. The density of the intake air, tough decreases. The decrease in inlet mass is less than the decrease in inlet ideal mass, so the volumetric efficiency increases. 7.3.2 Intake and exhaust system flow resistances When a gas (unsteady state) flows into a system of pipes, we will have friction, pressure and inertial forces are present. The relative importance of these forces depends on gas velocity and the size and shape of the pipes. Friction losses Because of friction losses induced by the flow, we have that the pressure inside of the cylinder is lower than the one inside of the inlet manifold, by an amount dependent on the square of speed. The total pressure 68  Figure 7.2: Volumetric efficiency as a function of the mean piston speed drop is the sum of the pressure losses in each component of the intake system. We are going to have losses even in a boosted engine (TC) in which the intake pressure is higher than the atmospheric one. The largest pressure drop is through the cylinder head ports and valves. As a result, the pressure pi in the cylinder during intake can be up to 20% lower than the intake manifold pressure. For each component we can apply Bernoulli’s equation: pj = ⇠⇢wj2 , where ⇠ is the flow resistance coefficient, which depends from the geometry of the component. The total pressure loss is ⇣ ⌘2 A then pa pi = ⇢u2 ⌃i ⇠j Apj = K⇢u2. Since u depends from the engine speed, also the pressure drop depends on it. With the same procedure, we can write the pressure drop in the exhaust system: pe pa = H⇢u2. From these two relationships, we can rewrite Equation 7.1:  1 (1 + Hu2 )(1 + Ku2 ) 1 v = 1 (7.2) Ku2 + 1 (rc 1) The pressure drops at the exhaust side are less significant than the ones at intake side. This is because we have the blowdown phase, in which a substantial part of burned gasses are expelled because of the pressure di↵erence between cylinder and exhaust system. In addition to that, the density at exhaust ports decreases with increasing engine speed, since there is less time for heat transfer to happen. 7.3.3 Intake system heat transfer As air flows through each intake port and past the hot intake valve (150 C) some heating of the intake air occurs, with consequent density decrease. as we have discussed in chapter 5, the heat transferred depends on the mean 69  Figure 7.3: Valve timing piston speed and on the density of the air at intake. In addition to that, the temperature of the mixture is further increased when the fresh charge meets the residual (hot) burned gasses. This has a negligible e↵ect on the volumetric efficiency, since the residual gasses cool down of the same measure and contract of the same amount. However, the heat transferred by the hot piston and cylinder walls is not negligible and causes a reduction in density up to 2%. This is another phenomenon that a↵ects the volumetric efficiency and it is called in-cylinder heat transfer. 7.3.4 Valve timing e↵ect In an air-fuel cycle valve events happen instantaneously at TDC and BDC. In real cycles, instead, the opening valve interval is higher than the cor- responding stroke for both intake and exhaust valves. This is due to the fact that the opening and closing of the valves cannot be instantaneous. In fact, the valves take some time to open and close (they depend on the cam) and they have to stay open for a time long enough to allow gasses through. There will be a moment in which both intake and exhaust valves are open at the same time. This moment is called valve overlap. Blowdown losses and influence on EVO timing In a real engine, we open the exhaust valve during the expansion stroke (around 30 to 70 CA before BDC). This is done in order to maximize the e↵ect of blowdown. We will loose some work in this way, but the pumping work will be smaller afterwards and the overall neat imep will be increased. The optimum timing for EVO varies with engine speed. In fact, we should open the valve earlier if the speed increases (the duration of the exhaust pro- cess decreases). Usually we cannot change the valve timing (fixed camshaft geometry) so we choose the optimal EVO at an intermediate speed. There are some engine geometries which can vary the EVO. 70 Valve overlap and induced charge The opening of the intake valve should occur sufficiently before TDC so that the cylinder pressure does not drop early in the intake stroke. The closing of the exhaust valve happens after the opening of the inlet one, in order to avoid the pressure of the burned gasses to rise near the end of the exhaust stroke. This means that we have a period of overlap. When the pressure of the gasses is higher than the pres- sure of the intake manifold, we have that some of the burned gasses en- ter the intake manifold, taking a volume Vi. Instead, when the pressure of the exhaust manifold is larger than the cylinder pressure (due to the expansion) some burned gasses re-enter the cylinder from the exhaust manifold, taking a volume Ve. The clearance volume of resid- ual gasses of the previous gasses is still present and has to expand before the fresh charge can come in. This means that the volume of cylinder that we have is in reality: Vd ( Vi + Ve + Vr ). The EVC Figure 7.4: Valve overlap and IVO are chosen in order to min- imize the overall e↵ect of the V and to maximize the induction of fresh charge. IVO typically occurs 10 to 25 CA before TDC while EVO occurs 8 to 20 CA after TDC. Ram e↵ect at high speed The mass of air inducted into the cylinder each cycle depends by the total pressure level p = p + 12 ⇢w2. At high engine speeds, the inertia of the gas in the intake system is still high when the intake valve is closing and increases the pressure in the port and continues the cylinder charging process as the piston slows down and approaches BDC. The intake valve is closed some 40 to 60 CA after BDC in part to take advantage of this so called ram e↵ect. With a closing delay like this one, a larger mass of air will get into the cylinder. Because of the flow’s inertia, the air might keep getting into the cylinder even if the cylinder pressure becomes larger than ambient pressure. Notice that the ideal IVC should be fixed at the moment when the velocity of the instantaneous inducted mass is zero. In reality, we need to also consider the reverse flow of fresh charge that will come back to the intake manifold 71 due to the piston motion towards TDC. By evaluating these two factors we can decide the optimum valve timing. We usually optimize the IVC timing for a particular speed n⇤. Reverse flow into the intake For speeds below n⇤ , the inertia of the flow is smaller and a net reverse flow into the intake manifold will occur. This flow is due to the motion of the piston back towards TDC in the compression stroke. Remember that the valve closes after BDC. The lower the speed the larger the reverse flow. The choice of n⇤ needs to be done taking into account this phe- nomenon. As we can see in Figure 7.5, as we increase the IVC crank angle, the positive e↵ect that is the ram e↵ect is shifted towards higher speeds. When we decide the IVC crank angle we need to take into ac- count this fact since we cannot have a too large speed because of the blowdown e↵ect that would occur at speeds lower than that, but we should also notice that a low crank Figure 7.5: E↵ect of IVC angle angle would mean losing the ram ef- fect at higher engine speeds. 7.3.5 Airflow chocking at intake valve This phenomenon is very relevant (and detrimental) at high engine speeds. We can consider the valve as a converging nozzle. In quasi steady-state conditions, the flow that we measure at the valve outlet should be the same one as the flow at the piston surface. Since we can consider the density as constants in both sections, we can say that the volumetric flow rate is the same: wIV Amin,IV = uAp At high u and for the valve only minimally open, we have that the velocity of the fluid at the valve reaches the speed of sound. This means that the valve is chocked. This means that the mass flow rate cannot increase any further even if we lower the pressure inside the cylinder (i.e. the piston goes down during the intake stroke). This phenomenon poses a limit to the maximum flow rate that we can have as the speed of the engine becomes greater. 72 7.3.6 Intake and exhaust tuning Inside of the intake and exhaust systems we have pressure fluctuations (due to the piston reciprocating motion) that increase in amplitude as the engine speed increases. The primary frequency of these fluctuations depends on the frequency of the individual cylinder intake and exhaust process. The cylinder motion generates a pulsating flow which sets up pressure waves in the intake and exhaust systems. These waves propagate at the local speed of sound. As the waves hit junctions and ends in the systems (ducts, plenums, manifolds and ports) they are reflected back towards the engine cylinder. We can say that the intake and exhaust systems are tuned if the reflected pressure waves aid the intake or the exhaust process. We can tune the system employing two e↵ects: 1. wave e↵ect: based on the length of the flow path; 2. resonance e↵ect: based on air duct and plenum geometry, it can cause the plenum pressure to oscillate as a Helmholtz resonator. Wave e↵ect If we have a pressure wave going into a duct, we can have two things hap- pening, depending on what the pressure wave meets when it reaches the end of the duct: it can meet a wall an be reflected back with the same sign or it can meet no wall and be reflected back with the opposite sign (if it was a wave that reduced the pressure now it will increase it). It is in this case that we would have a benefit. In fact, with the piston going down during the intake stroke, we have a pressure waves being generated. These are rarefaction waves, which reduce the pressure. When the wave reaches the intake manifold and it propagates towards the plenum (larger volume) it is reflected back through the manifold. This wave reaches the intake valve during the last part of the intake stroke, compressing the air and allowing more air mass inside of the chamber. The wave needs a certain time in order to get back to the intake valve 2L t= a where a is the speed of sound. We can increase (or decrease) the length of the pipe in order to have the proper timing of the wave. It needs to reach the inlet valve when we are in the second part of the intake stroke. We can tie the time to the crank angle and the engine speed in order to get the proper time given a speed and a crank angle: 2L ✓ = 6nt = 6n a 73 For a given crank angle and speed, we can get the right pipe length: ✓·a L= 12n We can see that at low engine speeds, we have longer pipes in order to have the timing tuned. We can use VIS (variable intake systems) in which we can choose two di↵erent pipes of di↵erent length depending on the speed of the engine. We can do a similar thing for the exhaust manifold in order to avoid having compression waves going back to the cylinders from the exhaust system. Resonance e↵ect This solution is good only for a small range of frequencies, so it is mainly used to reduce noise in the induction or exhaust pipes. It basically consists in making the plenum as a Helmholtz resonator. It is useful to also improve the volumetric efficiency at low engine speeds. A Helmholtz resonator is usually composed by a short tube connected to a totally enclosed cavity. The air in the neck of the tube is the piston, while the air in the cavity (cylinder) is compressed and expanded by it (adiabatically). Basically, we are creating a mass-spring system where the air in the cavity is the mass and the air in the neck is the spring. Our goal is to have the sequence of of intake processes to be tuned with the natural frequency of the resonator in order to exploit the oscillations to improve cylinder filling. We have that: pV = const and V dp + pV 1 dV = 0 ! dp = p dV V. Then dV = Adx. In PSAV07 (81-82) we have all of the steps. The end result is that the circular natural frequency of the system is r A !0 = a LVm where A is the area of the duct and Vm is the average cylinder volume. Obviously, the natural frequency is fH = !2⇡0. The maximum mass displace- ment is obtained when the ratio between the natural frequency and the engine revolutions is an even number. The absolute maximum is obtained for fH /fe = 2 ! fH = 2n. Values of the resonant frequency can be around 100Hz so the optimum engine speed in order to get an improvement on the intake process is around 3000 rpm. 7.3.7 Combined e↵ects on the volumetric efficiency In Figure 7.6, we can see the combination of the phenomena discussed in this section and their e↵ect on the volumetric efficiency. The thickest curve is the resulting volumetric efficiency as a function of the speed. Quasi-static phenomena are independent from the speed and drop the efficiency below 74  Figure 7.6: E↵ects on volumetric efficiency combined 100. We then have friction phenomena in intake and exhaust systems that change with the square of the speed. Charge heating during intake drops the efficiency while the positive ram e↵ect increases it. We have then the choking at high speeds which creates a steep decrease of v and then we have in-cylinder heat transfer which further decreases the efficiency. Finally, we have the positive e↵ect of tuning the intake and exhaust system. The most important factors that have an impact on the volumetric efficiency are the total flow friction, the IVC angle and intake tuning. The mean piston speed is the most relevant quantity. Figure 7.6 gives us the volumetric efficiency at wide open throttle (full load). For di↵erent loads, we have a di↵erent volumetric efficiency. For spark ignition engines, v decreases sharply with the load, while for compression ignition engines the volumetric efficiency is actually higher at idle conditions. this is because in a Diesel engine, we have less mass of fuel at smaller loads which means that we have lower temperatures which benefits the volumetric efficiency. In SI, instead, when we decrease the load we increase the flow losses on the throttle valve that is more closed. 7.4 Turbocharging and supercharging As we have said in previous chapters, supercharging an engine, means to increase the air (or mixture) density by increasing its pressure before it 75  Figure 7.7: Volumetric efficiency at di↵erent loads enters the cylinders. We have three methods of supercharging: 1. Mechanical supercharging; 2. Turbocharging; 3. Wave supercharging 7.4.1 Mechanical supercharging The mechanical supercharger is a separate crank-driven pump, blower or compressor which provides the compressed air. We can have several options like Roots blowers, sliding vane compressors, screw compressors, etc. The compressor is driven by the engine through some sort of connection. Modern superchargers can be driven by an eMotor, in order to decouple them from the engine’s speed. This way of supercharging gives rise to a very strong increment of bmep with respect to a NA engine, while it does not give any good contribution to the fuel conversion efficiency (it is lower than the one of a NA engine except for a small range). 7.4.2 Wave supercharging This method of supercharging is practically never used. It employs the wave action in the intake and exhaust systems to compress the intake mixture. The principle that is used is that if two fluids with di↵erent pressures in direct contact, the equalization of pressure happens much faster than the mixing of the two fluids. Basically, we put in contact the exhaust gasses (at higher pressure) and the fresh charge in a chamber which contains a 76 belt-driven bladed wheel. Since the exhaust gasses follow the pressure wave at lower velocity, only a very small amount of them mixes with the fresh charge and ends up in the cylinder. 7.4.3 Turbocharging In turbocharging, we use a turbine which is fed the exhaust gasses from the engine that powers a turbocompressor that compresses the intake air. Usually the turbine is centripetal and the turbocompressor is centrifugal. The use of an intercooler is very widespread. The work that we can ob- tain from the blowdown of the exhaust gasses is used to compress the air at intake. We have many advantages with turbocharging. First of all, we can reduce the engine packaging, weight and cost per unit delivered power. We can also reduce the total engine displacement (downsizing) since we can have the same mass of air in a smaller volume. We can increase the fuel conversion efficiency and improve the combustion process in Diesel engines and reduce engine noise. On the other hand, turbocharging increases the thermal and mechanical loads on engine components and enhances the risk of knock in SI engines. The torque profile that determines is not suitable for traction since it de- creases at lower speeds. Lastly, turbocharging introduces the so-called tur- bolag, which is a delay in the response of the engine in transient maneuvers. Compared to a NA engine, a TC engine has increased cylinder pressure and a larger cycle area, which positively a↵ects the bmep. With respect to a MS engine, a TC one has a lower increase in bmep but a much higher increase in fuel conversion efficiency. Turbolag In NA engines when the throttle pedal is pressed, there is little delay before the engine torque rises. In TC engines, instead, the air supply can rise more slowly (because of turbocharger inertia and transport delay of the air through the intake system). this means that we will have a reduction in the maximum torque that we can have during an acceleration, since we have this delay in air supply. The best way to keep the turbolag at minimum, is to have the polar moment of inertia of the turbocharger as small as possible. The impeller radius should thus be minimized. We can use turbocharger control to provide a good transient response. We have two methods for controlling the turbocharger. Boost control: wastegate If we have a fixed geometry turbine, it may be beneficial to have a bypass valve at the turbine inlet in order to have some exhaust gasses avoid the turbine. 77  Figure 7.8: E↵ect of turbolag Boost control: VGT VGT (variable geometry turbine) is a better way to improve the behaviour of the turbocharger. We have adjustable blades fixed on a a support ring at exhaust side. The blades can be rotated simultaneously by a pin. For low speed operation, the vanes are set to flat and result in a smaller cross-section for the exhaust gasses entering the turbine. The gasses flow faster and spin the turbine, promoting more fresh air in the cylinder at higher pressures. At high speeds, we have more exhaust gasses and we have a lower boost demand. This means that we can slow the gasses down by opening the vanes. Obviously we do not open the vanes completely (unless we are in an emergency). With respect to the wastegate solution, the VGT reduces the turbolag and provides higher torque. We usually adopt VGT for Diesel engines and wastegate for gasoline engines. 7.4.4 Volumetric efficiency of an engine with EGR In SC engines, we do not choose the ambient density as the reference one since we might have a v higher than unity, thus loosing any useful infor- mation about losses. Instead, we use the density at intake manifold. If we have EGR, we have also recirculated gasses in the intake system.The new volumetric efficiency will take care of that: ma + mEGR v = ⇢im Vd 7.5 Additional considerations on flow through valves and ports The intake port is generally circular and has a cross-section area that is no larger than the required one to achieve the desired power output. The ex- 78  Figure 7.10: Variation of flow area in a valve haust port, instead, needs to have a good valve seat and guide cooling, with the shortest length of exposed valve stem. The most important parts in valve opening is when the gasses start or stop flowing through the valve. The instantaneous flow through a valve depends from the lift (which, in turn, depends from the cam profile and timing) and from the geometrical parameters of the valve (head, stem, seat,...). We have three phases in a valve flow de- velopment, in which the valve lift in- creases. We can see the increase and Figure 7.9: Representation of a pop- decrease of the valve area in Figure pet valve 7.10. The three phases that we see in figure are: 1. Low valve lift ! The minimum flow area corresponds to a frustum of a right circular cone where the conical face between the valve and the seat, which is perpendicular to the seat, defines the flow area. 2. Second stage ! The minimum area is still the slant surface of a frus- tum of a right circular cone but the surface is no longer perpendicular to the valve seat. The base angle of the cone increases from 90 ( is the seat angle) toward that of a cylinder, 90. 3. Third stage ! When the valve lift is sufficiently large, the minimum flow area is no longer between the valve head and seat. It is the port flow area minus the sectional area of the stem. 79  Figure 7.11: Discharge coefficient 7.5.1 Flow rate and discharge coefficients We can imagine the valve to be a convergent nozzle thus allowing us to study the flow rate through it using the relationships that are used for the nozzles. Real gas flow e↵ects are taken into account by an experimentally derived discharge coefficient, CD. The mass flow rate through a valve is then v " ✓ ◆1/ u u 2 ✓ ◆ 1/ # C D AR p 0 p T t pT ṁ = p 1 r T0 p0 1 p0 The term CD AR = Ae represents the e↵ective area that is smaller than the geometrical one, due to various real e↵ects. We can use di↵erent reference areas like the valve head area or the port area at valve seat, the geometrical minimum flow area (difficult to evaluate) or the curtain area ⇡DV LV. The most convenient reference area to choose is the curtain area, which varies linearly with the lift of the valve. The discharge coefficient based on the valve curtain area is a discontinuous function of the valve lift to diameter ratio. At low lifts, the flow remains attached to the valve head and seat, giving high values for the discharge coefficient. At intermediate lifts, the flow separates from the valve head at the inner edge of the valve seat. At this point, CD drops abruptly. It then increases with larger lifts since the size of the separated region remains approximately constant while the minimum flow area is increasing. It has been shown that over the normal operating engine speed range, steady-flow discharge coefficients can be used to predict dynamic performance with reasonable precision. Obviously, under dynamic operation, the change in CD happens at slightly di↵erent valve lifts. At high engine speeds, tough, the flow might become chocked. We can use 80 various definitions of inlet chocking (based on the Mach number) but what we use to correlate the volumetric efficiency and the inlet valve design is the Mach index, Z (also called gulp factor) ✓ ◆2 Ap u u B 1 Z= = C i Ai a a DV Ci where: Ai is the nominal inlet valve area, Ci is the mean valve discharge coefficient, based on the area Ai and a is the speed of sound. The parameter Z corresponds closely to the mean Mach number in the intake valve throat. Using the Mach index as an independent variable, the pattern of v for di↵erent engines that have the same intake valve opening and closing time is very similar. This makes Z a sort of geometrical similarity parameter. 7.6 Variable valve timing and actuation Variable control of valve operation as a function of engine load and speed is being increasingly used instead of fixed valve timing. The simplest approach at the variable valve operation is VVT: variable valve timing. We have a rotation of the camshafts relatively to the crankshaft. This method varies the phasing of the intake and exhaust camshafts via a cam phaser in order to improve the engine’s airflow capability and increase torque at low speed. A more sophisticated approach is the variable valve actuation, VVA. These mechanisms can control the valve timing, open duration and lift. Controlling the exhaust valves has some additional benefits like reaching a state similar to a Miller cycle and reduce N Ox emissions. Variable valve control also has the potential for reducing the engine pumping work at lighter loads: Early IVC at low speeds decreases backflow of air into the intake during the early part of the compression stroke; Late IVC increase the air charging of the cylinder at high speeds and allows the piston speed to be increased before the chocking limit is reached. This can lead to engine downsizing. One simple control method in multi-cylinder gasoline engines is to cut out a number of cylinders at lighter loads (4 out of 8, 2 out of 4,...). The The displacement volume of the firing cylinders is reduced with an increase of pressure in the manifold and a reduced pumping work. The friction in the cylinders that are not firing is still present and has to be overcome. The net result is a slight benefit in terms of fuel consumption. 81 7.6.1 Cam phasing A common approach is to continuously adjust the phasing of intake and exhaust cams relatively to the camshaft. The typical range of cam adjust- ment is about 40 CA, around a point which is 50 above BDC. This can give some useful benefits. At idle conditions, the camshafts are set for late IVO and early EVC, in order to reduce the overlap period and thus, the exhaust backflow in the cylinder. At low to mid speeds, the intake cam is rotated to close the intake valve early. At high speeds, we retard IVC to take advantage of the ram e↵ect. In order to achieve this control, we use multiple cam profiles (lower lift, lower duration at low speed and higher lift, higher duration at high speeds). 7.6.2 Pumping work reduction Variable valve control can reduce the pumping work loss. In fact, the mass in the cylinder is given by the ideal gas law, applied at the intake valve closing location. As the IVC angle changes, we need the same mass of fuel and air in order to produce the torque. As the volume of IVC becomes smaller, the intake pressure must be increased, thus reducing the pumping work. Early IVC reduces the compression stroke work through gas expansion during the second part of the intake stroke. With late IVC (very late) the pumping work is essentially eliminated. 82