Diesel Engine Fundamentals
New emission regulations and performance requirements imposed on modern diesel engines are strong motivators for new technology. Traditional design methods and parameters are continuously being upgraded and new ones adopted to meet the competitive market pressures. However, to those who are involved in modern engine designs, a good knowledge of the many aspects that not only control the engine performance, but also its emissions profile is imperative. This knowledge must evolve from simple design principles to sophisticated interactions between various engine systems as well as its post-combustion exhaust emissions control devices.
In this paper a review of the basic engine components, design parameters, geometric properties, and performance issues are presented. These parameters are discussed with the view to maximize performance and fuel economy and minimize exhaust pollutants. While many of the principles discussed in this paper may have application to other powerplants, the main emphasis is on diesel engines.
Heat engines can generally be considered energy conversion machines. In essence, chemical energy supplied generally in the form of fossil fuel to a heat engine is combusted by mixing with oxygen provided the right temperature is available and produces heat that is eventually converted to useful work.
Heat engines can be
External combustion engines, or
Internal combustion engines.
Examples of the external combustion engine include the Stirling engine where heat is added to the working fluid at high temperature and rejected at low temperature (compare "The Case..."). A net work is produced by the working fluid. Heat added to the working fluid can be generated from practically any heat source, such as burning fossil fuels, wood, or any other organic material. The steam engine is another example of external combustion systems. Heat added from an external source elevates water temperature until it is converted into steam that provides pressure and eventually the net work. Steam engine powered cars in the
In internal combustion engines, the same combustible mixture that produces heat is responsible for producing useful work. Two basic categories of internal combustion engines can be classified as rotating and reciprocating engines (compare "The Case..."). A very well known example of the rotating engines is the Wankel engine which is also known as the rotary engine. A clear example of the second category is the reciprocating engines which in itself can be divided into two types: the two-stroke and the four-stroke engine. In internal combustion engines, the working fluid is the combustible mixture of air and fuel. This fluid is responsible for releasing heat energy that is stored in the fuel and producing useful work. Worthwhile goals common to the design and development of all heat engines include: maximizing work (power output), minimizing energy consumption, and reducing pollutants that may be formed in the process of producing work. Figure 1 shows the main components of a reciprocating engine. Intake and exhaust valves are omitted for simplicity, however it is worth noting that in some two-stroke engine designs inlet and exhaust ports are used rather than valves which are commonly used in four-stroke engines.
Both internal combustion reciprocating engine categories (two- and four-stroke) may be equipped with either a spark-ignited combustion system, also known as SI, or a compression-ignited system known as CI. Spark-ignited engines use a combustion cycle known as the Otto cycle, while compression-ignited engines use the Diesel cycle. Spark-ignited systems are characterized by homogeneous or mostly well mixed charge of fuel and air. In this medium combustion is initiated by a spark and the flame propagates along a front from the spark location to the opposite side of the combustion chamber. Diesel engines achieve their high performance and excellent fuel economy by compressing air to high pressures then injecting a small amount of fuel into this highly compressed air. The charge of air and fuel in these engines is described as heterogeneous meaning that the fuel remains separate from the air for a finite time in the combustion chamber. Heat generated due to the compression of air in the cylinder causes the small amount of highly atomized injected fuel to evaporate. Mixing with the hot surrounding air in the combustion chamber, the evaporated fuel reaches its auto-ignition temperature and burns thus releasing the energy that is stored in that fuel. The auto-ignition temperature of fuel depends on its chemistry. Unlike the SI system, combustion in compression-ignited engines occurs at many points where the A/F ratio and temperature can sustain this process.
Operation of Reciprocating Internal Combustion Diesel Engines
Reciprocating internal combustion diesel engines can be classified as two-stroke or four-stroke designs. In the following sections, the operation of each classification is described and some of the parameters affecting performance are detailed.
Principle of Operation
By definition, two-stroke engines require two strokes to complete their combustion cycle. Figure 2 gives the details of the two-stroke combustion cycle. With the transfer and exhaust ports open, air under slight pressure in the crankcase flows into the cylinder. The rising piston eventually covers the transfer ports, thus trapping the inducted air into the cylinder. Further upward motion toward top dead center compresses the air where fuel is injected at the appropriate timing. Heat absorbed from the surrounding hot compressed air causes the fuel to evaporate and mix with the air. Once the auto-ignition temperature is reached, combustion begins and causes the working fluid (combustible mixture) to expand thus applying pressure on the surface of the piston thus producing useful work at the engine output shaft. Meanwhile, fresh air flows into the crankcase to be compressed by the descending piston on its way to bottom dead center. While descending, the piston uncovers the exhaust port starting the scavenging of the cylinder and causing a slight increase in crankcase pressure. This increase in crankcase pressure causes the fresh air induction into the cylinder through the transfer port and resumes the cycle once again.
Scavenging in Two-Stroke Engines
The process of purging exhaust gases from a previous cycle and filling the cylinder with fresh air for a new cycle is referred to as scavenging. The main method for scavenging two-stroke engines is by using the pressure of the inducted fresh air to purge or displace the burned gases from the previous cycle. Generally, the greater the oncoming air pressure, the more complete the scavenging process. Therefore, better scavenging in two-stroke engines is achieved, in part by raising the pressure of fresh air being inducted into the cylinder. This process is accomplished by using various devices such as blowers, compressors, or pumps.
Scavenging in two-stroke engines is performed mainly by one of three methods:
There are other variations to these three methods, but these remain the principal implementations of scavenging in two-stroke engines. Figures 4 (a), (b), and (c) illustrate the differences between the three methods.
As the exhaust ports open (EPO), a rapid drop in cylinder pressure is observed. Evacuation of the exhaust gas through the exhaust ports is known as the blowdown process. A blowdown angle is defined as the angle between EPO and the angle at which cylinder and exhaust system pressures equalize. The inlet ports open (IPO) late into the blowdown process and allow fresh air to enter into the cylinder. This step can begin only when the fresh air charge pressure exceeds that of the cylinder. Meanwhile, the piston reaches its bottom dead center (BDC) position and reverses its direction thus moving towards its top dead center (TDC). The point at which the piston reverses its direction is shown as BC (bottom center) in Figure 6.
The next event in the cycle is the inlet port closing (IPC) which takes place as the piston moves towards its TDC and covering the inlet ports. Further piston movement towards its TDC causes the exhaust ports to close (EPC) thus trapping the fresh charge and any residual exhaust in the cylinder. Thereafter, a steady but fast pressure rise is observed in the cylinder. This pressure rise is also accompanied by a proportional increase in temperature. The crank angle during which both inlet and exhaust ports remain open is referred to as scavenging angle.
The description given to the scavenging process so far was somewhat ideal and comprised distinct steps. However, the actual scavenging in two-stroke engines is far less than ideal. In fact, during scavenging not only does the fresh charge exchange heat with the residual gases, it also mixes with it and changes its chemical composition in the process. The final chemical make up of the mixture at the end of the scavenging process plays an important role in the combustion quality as well as its resultant emissions. An inherent loss in two-stroke engines results when some fresh charge escapes through the exhaust ports during scavenging. This phenomenon is often referred to as short-circuiting which leads to lower volumetric efficiency.
A two-stroke is usually smaller in size than a four-stroke engine having the same power output and tends to have higher specific power (power output for a given engine displacement) than its four-stroke counterpart. Two-stroke engines are generally less fuel efficient than four-stroke engines. The main reason for this relative fuel inefficiency in two-stroke engines is poor scavenging and relatively low volumetric efficiency.
Basic Performance Parameters in Two-Stroke Engines
Having described the two-stroke combustion cycle, we can now define several parameters that would help assess engine performance.
Compression ratio is generally defined as the ratio of total (maximum) to minimum cylinder volume. According to this general definition, compression ratio is the product of dividing the cylinder volume when the piston is at BDC by the cylinder volume when the piston is at TDC. This definition complies with the traditional or conventional understanding that applies to reciprocating internal combustion engines.
It is worth noting however that the traditional definition may not reflect the actual compression ratio in two-stroke combustion systems. In fact, compression is almost non-existent until the piston covers both inlet and exhaust ports in two-stroke engines. Therefore, a more accurate definition of compression ratio in two-stroke engines should limit the total cylinder volume to that in effect at the time of exhaust port closure when the working fluid is trapped within the cylinder. In spite of this technicality, the traditional definition of compression ratio is still preferred over other alternatives. Therefore, compression ratio can be defined as follows:
(1)Cr = (Maximum Cylinder Volume)/(Minimum Cylinder Volume)
Compression ratio is an important parameter by which engine efficiency can be determined. While the overall efficiency of the engine may depend on a number of other parameters such as mechanical efficiency, volumetric efficiency, and pumping efficiency to name a few, compression ratio has a direct impact on thermal efficiency. Equation 2 (also reported in The Case...) shows the mathematical relationship between compression ratio and thermal efficiency.
(2)ηth = [1 - 1/Crγ] × 100
ηth - thermal efficiency,
Cr - compression ratio, and
γ - the ratio of specific heat at constant pressure to the specific heat at constant volume.
It follows then that the greater the Cr, the higher the thermal efficiency of an engine.
For an engine cylinder having a bore Bcyl and a piston stroke Sp, the swept volume (Vs) is defined by the product of the cross-section area of that cylinder (πBcyl2/4) and the piston stroke (Sp), as follows:
(3)Vs = (πBcyl2/4) × Sp
Clearance volume (Vc) is the volume above the piston when it is at its TDC position. The swept and clearance volumes (both terms are illustrated in Figure 7) are used to define compression ratio. Equation 4 is used to determine the geometric compression ratio of an engine:
(4)Cr = (Vc + Vs) / Vc
The delivery ratio is the ratio of the mass of fresh air delivered during the scavenge duration and the mass of air required to fill the swept volume at ambient conditions. The mass of air required to fill the swept volume at ambient conditions serves as reference and is conventionally calculated on the basis of the prevailing ambient pressure and temperatures conditions.
(5)Dr = (Actual Air Mass Delivered During Scavenge) / (Reference Air Mass to Fill Vs)
The delivery ratio defines how well an engine is able to fill the cylinder with air from the prevailing ambient conditions. Obviously the more air is introduced into the cylinder the more oxygen is available to the combustion process. Even though the majority of the air inducted into the cylinder may not engage into the combustion process, still the opposite action of starving a diesel engine from air may have devastating consequences on combustion efficiency. The evidence of a diesel engine starved of air is usually in the form of black smoke that is very visible.
The scavenge ratio (Sr) is the ratio of the mass of fresh air supplied during the scavenge duration and the mass of air required to fill the total cylinder volume at ambient conditions in naturally-aspirated engines. The mass of air required to fill the total cylinder volume at ambient conditions serves as reference and is conventionally calculated on the basis of the prevailing ambient pressure and temperatures conditions. Scavenge ratio should not be confused with the delivery ratio, the difference being that in the scavenge ratio the reference is total cylinder volume as opposed to just the swept volume in the case of the delivery ratio.
(6)Sr = (Actual Air Mass Delivered During Scavenge) / (Reference Air Mass to Fill Total Cylinder Volume)
Naturally, a successful scavenge is required before we can introduce the maximum amount of air in the cylinder. Therefore, good scavenging is a prerequisite for a good delivery as well as good scavenge ratios.
The working fluid in the cylinder at the point of exhaust port closure may consist of trapped fresh air (mfa), residual air from a previous cycle that had not engaged in the combustion process (mra), and exhaust that had not been scavenged (mex). The scavenge efficiency (Se) is the ratio of the trapped fresh air to the total mass trapped in the cylinder.
(7)Se = mfa / (mfa + mra + mex)
Purity of Charge
It is important to differentiate between the term purity of charge (Pu) and scavenge efficiency. These terms are often confused with each other. Charge purity is the ratio of the air trapped in the cylinder at the start of combustion, to the total mass of the working fluid. The air trapped in the cylinder prior to combustion consists of the charge of fresh air trapped (mfa) plus any residual fresh air that had not engaged in prior combustion (mra).
(8)Pu = mfa / (mfa + mra)
From a combustion efficiency stand point it is important to utilize as much of the fresh charge inducted into the cylinder as possible. In other words we would hope to have an extremely small mra if any. Ideally, the highest purity of charge is achieved when all of the charge is consumed during the combustion process.
The trapping efficiency (Te) is defined as the ratio of the charge retained in the cylinder to the charge supplied. This definition applies at the point of port closure at which the charge is trapped within the volume of the cylinder. The higher the Te, the higher the fresh charge trapped together with its oxygen content being made available to the combustion to follow.
(9)Te = (Mass of
There may be other design parameters that could be defined having direct implications on engine performance and emissions characteristics. However, the preceding are the more common and often used.
Scavenging Characteristics in Various Two-Stroke Designs
It may be useful at this point to apply some of the definitions to various scavenging methods and examine how well these concepts may meet design objectives. Figure 8 shows scavenging behavior in large two-stroke diesel engines for three scavenging configurations.
The line showing perfect displacement indicates that the fresh charge has displaced all of the exhaust products from the prior combustion cycle and the entire cylinder volume is being occupied by a fresh charge. This line also implies that there was no mixing between the fresh charge and the products of combustion that were scavenged. On the other end of the spectrum, complete mixing may take place when the scavenging process allows enough interaction between the fresh charge and the products of combustion. Obviously, one should aim for perfect displacement as the design objective. Examination of the results shown in Figure 8 indicates that uniflow scavenging is the most effective followed by loop scavenging and then cross scavenging.
Operation of Four-Stroke Engines
It takes four strokes to complete the combustion cycle in four-stroke engines. Figure 9 is a schematic representation of the four-stroke combustion cycle as applied to a diesel engine. In the first stroke, the intake stroke, the piston moves from its position at top-dead-center (TDC) toward the bottom-dead-center (BDC). During most of the intake stroke, filtered air is inducted into the cylinder. In the second stroke, air that was inducted into the cylinder is compressed by the piston moving back to TDC from its starting position at BDC. This second stroke is known as the compression stroke where air in that cylinder heats up to a temperature usually above the auto-ignition temperature of the fuel which is injected into the cylinder near TDC. As the fuel burns, heat energy is released raising the pressure inside a greatly reduced volume near TDC. This energy release produces pressure that is applied to the top surface of the piston thus pushing it back toward its BDC.
This stroke is known as the expansion stroke since it is through that expansion that power (pressure) was imparted to the piston and caused it to move to BDC. The expansion stroke is also known as the power stroke for obvious reasons. It is also referred to by some as the work stroke since the expanding gases were producing work by applying their pressure to the top of piston. The last of the four strokes is the exhaust stroke where combustion by-products are exhausted into the exhaust system for evacuation into the atmosphere. In general, today's four-stroke diesel engines are equipped with devices that enhance air charging and allow injecting additional fuel in amounts proportional to the additional air inducted to improve specific power output.
Changes in pressure, volume, temperature, and mixture composition occur during the four strokes. The pressure-volume diagram is often used to describe changes in pressure and volume in the cylinder during a complete cycle. Figure 10 illustrates pressure and volume changes for a naturally-aspirated diesel engine.
In Figure 10, intake and exhaust valve events are marked by points 1 through 4, where Point No. 1 is the point at which intake valve opens, Point No. 2 is intake valve closing, Point No. 3 is exhaust valve opening, and Point No. 4 is exhaust valve closing. It is important to note that both intake and exhaust valves remain open during the time between Points 1 and 4 as well as its equivalent crank angle duration. This period is referred to as valve overlap and plays an important role in engine performance and its emission characteristics.
The intake valve closing occurs a few degrees beyond BDC to improve cylinder filling and therefore, the volumetric efficiency of the engine. Effective and rapid compression of the working fluid (air) begins after intake valve closing as the piston travels from BDC to TDC. In naturally aspirated engines, pressure inside the cylinder during the intake stroke is below atmospheric pressure. Restrictions through the air intake filter, air inlet piping, intake manifold, intake port, and intake valve contribute to pressure loss and help reduce cylinder pressure to below atmospheric. Shortly following combustion, the expansion stroke begins and is marked by a number of chemical reactions and heat transfer processes while the piston travels from TDC to BDC. At Point No. 3, the exhaust valve opens thus allowing some of the combustion products to go through a blowdown process as a result of the pressure differential between the cylinder and the exhaust system. The remainder of the exhaust gases are expelled from the cylinder by virtue of the piston motion from BDC to TDC during the exhaust stroke.
ID - ignition delay; EVC - exhaust valve closing; IVC - intake valve closing; TDC - top dead center; BDC - bottom dead center; EVO - exhaust valve open; IVO - intake valve open
Another way to illustrate the four-stroke cycle is through the Pressure-Crank angle diagram shown in Figure 11. In addition to the details outlined in the description of the pressure-volume diagram, the pressure-crank angle diagram (Figure 11) highlights the point at which fuel is injection (I) as well as ignition delay. During this delay fuel injected into the cylinder evaporates using heat from the working fluid that had been compressed. The result of the heat transfer from the compressed air to the fuel is a reduction in the rate of pressure rise that is illustrated in Figure 2.11. Following the start of combustion, the rate of pressure rise increases dramatically and the combustion pressure peaks a few crank angle degrees past TDC. Factors controlling the rate of pressure rise include: the ignition delay, fuel quality, and the rate of injection. In many designs, the engine noise, vibration, and harshness characteristics is often tied to the rate of pressure rise in the cylinder.
Together with the rise in cylinder pressure, cylinder temperature also increases and reaches its peak. The maximum combustion temperature depends on several factors including: fuel rate, fuel injection timing, fuel quality especially its calorific value and cetane number, initial cylinder pressure at intake valve closing, and charge temperature.
So far intake and exhaust valve motion has been treated generally in relation to the specifics of the pressure-volume or pressure-crank angle diagrams. Earlier, valve overlap was cited as a parameter having major influence on engine performance and its emission characteristics. A more detailed look into the opening and closing of these two valves reveals more insight into their effect on volumetric efficiency and total charge composition. Starting with the exhaust valve, its opening takes place at a point near the end of the power stroke. The timing of EVO should not be too early lest useful work is lost, yet it is beneficial to effect the valve opening while cylinder pressure is at a level capable of clearing exhaust products through the exhaust valve area during the blowdown time. To ensure complete clearing of the exhaust gases through the exhaust valve opening it is usually kept open e few degrees past TDC. It is worth noting that both valves do not reach their fully open position instantaneously, but have a finite length of time during which they move from a fully closed to fully open position. To make the best use of both valves they must be in their fully open position at the time when they are exposed to the maximum pressure differential causing the working fluid to flow across them. To ensure this aspect of the cylinder filling and emptying processes, the intake and exhaust valves are usually opened before the start of the intake and exhaust strokes, respectively. They are also held open a few degrees past their respective strokes for the same purpose. As the exhaust valve is opened exhaust gases are expelled by their own kinetic energy, thus reducing the work required by the piston during the exhaust stroke to expel the remaining exhaust gases. Ensuring the expulsion of all exhaust products from the cylinder facilitates the induction of a fresh and generous charge to sustain combustion of the tiny quantity fuel injected into the cylinder. The intake valve opens towards the end of the exhaust stroke while exhaust gases are exiting through the exhaust valve at high velocity. Their high exit velocity creates a pressure drop in the cylinder that helps draw the fresh charge and maximizes induction. If the intake valve opening is too early, some of the exhaust products may actually flow back through its opening into the intake port and then on to the intake manifold. This portion will be inducted once again into the cylinder during the intake stroke and contaminates the fresh charge with exhaust. The proper function of both valves may require timing their opening and closing in a way that may interfere with the piston position. In such cases two solutions may be used: valve recess in the cylinder head as shown in Figure 12 or valve cutouts in the piston crown as shown in Figure 13. Therefore, it is extremely important to carefully design the timing of intake and exhaust valve opening, closing, lift, flow area as well as intake and exhaust valve overlap.
There are two basic types of four-stroke diesel engines: the direct- and the indirect-injected engines. The design and operation of both types was described in “The Case for the Diesel Engine” paper, where basic differences in their construction were explained. Recent interest in energy conservation has caused most if not all new four-stroke diesel engine designs to adopt the direct-injection concept for its superior fuel economy and its future promise of low emissions.
In spite of the promising future for direct-injected diesel engines, the indirect injected engine (IDI) clearly dominates the passenger car market. This dominance is due to its relatively quiet and smooth operation when compared with older direct injected diesels. In addition, IDIs have higher power density than DIs and are characterized by lower nitric oxide emissions than its DI counterpart. IDI engines are more popular around the world than they are in the
Although IDI engines have lower combustion noise, less costly fuel injection system, higher power density, and in general lower emissions levels, HSDIs have better startability in cold weather, less heat rejection to the water jacket, more EGR tolerance, greater durability, and lower overall carbon dioxide emissions.
Other Classifications of Engines
So far we have treated reciprocating engines as either spark- or compression-ignited engines. We have even subdivided compression-ignition engines into two categories. By so doing, we obviously run the risk of over simplifying engine categorization. Therefore, to put this potential misunderstanding to rest we need to mention here that there are many other ways by which engines can be categorized. Engines can be categorized by the following characteristics:
Mobility: Engines can serve both stationary as well as mobile applications. Stationary engines range from very small power outputs perhaps below 2 horsepower such as Hatz single cylinder engines to as high as 21,000 horsepower such as the Harland and Wolff uniflow-scavenged two-stroke engine pictured in Figure 14. Stationary engines may be used as power generation either as standby or continuous applications. They are also used in driving machinery such as large compressor that specialize in moving bulk.
Fuel: So far we have mainly addressed engines that use either gasoline or diesel fuels. Yet, fuels are not necessarily limited to these two, but include others such as compressed natural gas (CNG), liquid propane gas (LPG), methanol, ethanol, biodiesel, broad-cut, kerosene, dimethyl-ether, and a number of others. The less common fuels may be used in special applications that may be located near an abundant supply of that fuel.
Application: Engines may be installed in vehicles serving off road or on highway applications. Off road engines may cover multiple applications ranging from earth-movers, back hoes, and other construction equipment to agricultural machinery such as combines, tractors, mowers and garden tools. On highway engines may power heavy trucks as well as passenger cars and mopeds. Other applications that do not quite fit the description of on highway or off road may include aircrafts, marine, locomotive, and portable units.
Configuration: Engines are designed to fit a variety of installations. For many years in-line engine designs (see Figure 15a) were most popular for vehicular applications. Yet, in the mid-1970's, front-wheel drives became popular to provide more room in the new downsized car designs. Transverse engine installations became common practice and led to rash of conversions to vee engine configurations (see Figure 15b) from the in-line designs. The vee configuration compressed the length of the engine and allowed its packaging under the hood of the passenger car. Other configurations include horizontally opposed piston (see Figure 16), radial (see Figure 17a) for aircrafts, and delta (see Figure 17b).
Valve/Port Design: The position of intake and exhaust valves or ports can be used to differentiate among various engine designs. For instance, overhead cam design facilitate the actuation of unit injector fuel injection systems. Actuation of the unit injector is often accomplished by inserting an additional cam between the intake and exhaust cams. Figure 18 shows a variety of cam arrangements as applied in practical engine embodiments.
OHV - overhead valve; OHC - overhead cam; DOHC - dual overhead cam
Induction: Induction systems come in two basic designs; naturally-aspirated or turbocharged. Hence, engines that do not have devices to boost their charge are referred to as naturally-aspirated and those that have charge boost devices, such as turbochargers or superchargers, are called turbocharged engines. Figure 19 is an illustration of a turbocharged engine.
Charge Air Cooling: Turbocharging or supercharging engines leads to increasing charge air temperature and reducing its density. To improve charging of the combustion chamber, designers resort to cooling the charging after it had been boosted (increasing its pressure), hence the term aftercooling is used to describe a system through which air passes through a charge cooler, as illustrated in Figure 19. In the aftercooler heat is exchanged to another medium, normally water or air, prior to its introduction into the cylinder. Engines are often described as turbocharged and aftercooled (TA). Some designers refer to this heat exchanger as an intercooler since it is placed between the turbocharger and the intake manifold of an engine or port of a cylinder.
Engine Cooling: Combustion produces heat that must be dissipated away from the engine hottest regions to preserve its mechanical integrity. The process of carrying heat away from the engine's critical component is achieved through its cooling system. While most engines use a water jacket around the hot engine parts to transfer the heat from the engine to the environment via a heat exchanger (radiator), some engines use air cooling. The liners in these engines have fins on their outer surface that exchange heat by means of air blowing across those fins.
Power Modulation: Increasing or decreasing the engine's power output generally requires controlling its air-to-fuel ratio. In gasoline, spark-ignited engines power modulation is achieved through throttling the engine, thus reducing its air flow and enriching its fuel and air mixture. Some engineers refer to this method as qualitative control since it involves changing the quality of the fuel/air mixture from lean to rich or vice versa. On the other hand, compression ignition engines have an overall lean mixture at all operating conditions. They are referred to as quantitatively controlled engines since power is controlled by varying the amount of fuel in an engine where air flow is mostly unchanged for a fixed speed.
There are several other designations that could be considered categories of engines, but they are a bit more technically involved and used by those who are well versed with engine designs. These designations may include the type of combustion chamber used in an engine, such as M.A.N chamber for a system having a design specific to a German company (shown in "The Case..."), or Quadram for a system designed by Perkins. Other designation may refer to the method of mixture preparation, and so on. Yet, the preceding classification or categorization covers most of the designs available.
Assessment of Engine Performance
Regardless of categories, design features, importance of application, displacement, or any other descriptive feature engines must perform a certain task. It is reasonable to expect engines to give maximum performance at minimum cost. In other words, what return should customers expect on their capital investment (price paid for the engine and its installation), and their operating cost (cost of running and maintaining the engine). In addition and in view of current and future environmental concerns, it is not enough to maximize performance and minimize cost, but to do so while preserving the environment.
It is perhaps time that we investigate engine performance through applying thermodynamic principles. This material is presented in a simplified manner to facilitate it understanding especially to those not familiar with this science. The fundamental reason for resorting to thermodynamics is that it is an elegant way to treat the balance of energy as well as mass of the working fluid in a controlled volume. The controlled volume in this case is the cylinder where energy and mass flow into and out of. Figure 20 is an illustration of the control volume in an engine where both chemical energy in the form of fuel as well as mass in the form of fuel and air are introduced.
Fuel is usually metered into the control volume where air is also inducted. Both fuel and air are introduced into the cylinder in amounts (mass) that support efficient combustion and produce the desired power output. In summary, the control volume receives mass and energy and also delivers mass and energy. Applying the laws of thermodynamics helps in quantifying the relationship between the energy delivered to that received by the control volume.
The First and Second Laws of Thermodynamics
The first law of thermodynamics simply states that energy cannot be created nor destroyed but can only be converted from one form to another. For instance, a mass of hydrocarbon fuel contains chemical energy that is converted to work or mechanical energy within the cylinder (control volume) of an internal combustion engine. Theoretically, if this process was ideal and no losses are incurred this energy conversion would be 100% efficient. Yet, in reality converting energy from one form to another involves many losses resulting in an overall loss in efficiency. This fact is what the second law of thermodynamics expresses as it states that the useful work from a combustion system should be less than the energy input [Henein 1985]. In general, the ratio between useful work and the thermal energy added to the control volume represents the brake thermal efficiency of the system. Considering the cylinder and piston arrangement shown in Figure 20, the combustible mixture of fuel and air is burned in the control volume producing heat that results in the expansion of that volume causing the piston to move. Motion of the piston creates friction against the cylinder walls leading to friction heat loss. Another source of loss results from the temperature associated with the heat generated by the combustion process itself. As the combustion temperature increases, the cylinder material approaches its limitation in mechanical strength. Therefore, cylinders or control volumes are cooled, by water or air, to move heat away from the material thus preserving its mechanical strength. Heat transferred away from the control volume material is another loss added to the balance between the energy received by that control volume and the energy it delivers back. Another major source of loss in this energy conversion system is exhaust gases flowing out of the control volume. Exhaust gases exit the control volume with heat energy delivered to ambient without any benefit. They also exit with a great deal of potential energy (pressure) as well as kinetic energy (speed). Therefore, considering the system on hand we can think of a control volume where fuel and air are supplied and in return piston motion (work) is delivered, but the work delivered is much less than the value of energy supplied to the control volume. The difference between the energy supplied to the control volume and that it delivers is the sum of losses including, but not limited to, cooling and exhaust losses. A helpful illustration of this balance of energies is given in Figure 21.
While the description given so far for the energy exchange through a control volume is generally correct it may not be very complete. A better accounting of all the energies entering and leaving the control volume will have to include other types of energies yet unaccounted for. For instance, any mass entering the control volume brings with it several forms of energy:
internal energy; mainly due to its temperature which is generally very small
kinetic energy; mainly due to injection characteristics which usually leads to important interactions between the fuel and air within the control volume
potential energy; generally associated with pressure admitting mass into the control volume
flow energy; principally associated with the inter-relation between the control volume and its pressure.
Revisiting the first law of thermodynamic and considering the various forms of energy we are now acquainted with, one could think of the energy balance in a control volume as follows:
(10)Net Output = (Energy Supplied to the Control Volume) - (Total Energy Loss)
In other words, a careful accounting of the energies supplied to the control volume and those delivered by the same volume can assist in assessing the system conversion efficiency. Caution must be exercised when defining the control volume. So far, we have considered one cylinder in an engine as the control volume. However, an entire engine or the total vehicle can be viewed as that control volume. Therefore, defining the control volume and its boundaries is extremely important in the energy conservation equation.
Mass Conservation in Combustion Thermodynamics
Combustion Mass Balance
To complete the discussion regarding the control volume, consideration should be given to the mass entering and leaving it. As illustrated in Figure 20, fuel and air are the two principal constituents entering the control volume. In view of modern diesel engine technology this may be a limited treatment of the masses entering the control volume since the need to control emission may dictate recirculating some exhaust products back into the cylinder. In addition, lube oil contribution to exhaust emissions is being scrutinized and efforts are made to limit its consumption within the cylinder. Therefore, a more accurate representation of the mass balance in a control volume may be described by the following relationship:
(11)Exhaust Mass = Mass of Air + Mass of Recirculated Exhaust + Mass of Fuel + Mass of Lube Oil
(12)Mexh = Ma + Mf + Megr + Mlo
In practical embodiments of reciprocating internal combustion engines accessories are used to perform various functions in support of the engine operation. For example, lubricating the engine requires a oil pump driven by the engine itself, thus subtracting a portion of the work produced by that engine. Therefore, if the control volume is the cylinder then the conversion efficiency of such system will be higher that if the control volume was an engine. In fact, in diesel engines power is consumed in driving its fuel injection system. Other drives that are required for the engine operation include the camshaft, alternator, coolant pump, and superchargers.
Diesel Fuel Composition
Even though combustion in diesel engines is not the subject of this discussion, an alternative treatment of the mass balance in a control volume, cylinder in this case, can be helpful. A simplified expression for mass conservation can be limited to reactant species and reaction products such as fuel (CnHm) and air (mostly nitrogen and oxygen) reacting with each other in the proper environment and producing exhaust constituents as follows:
(13)CnHm + aO2 + 3.76aN2 → bCO2 + cCO + dH2O + eOH2 + fH2 + g(HC) + hNO + iHCHO + jNH3 + kN2
In Equation 13, CnHm represents hydrocarbon fuel reacting with air consisting of oxygen and nitrogen in a volumetric ratio of 20.99 to 79.01%, respectively. It follows that for every mole of oxygen provided, 3.76 moles of nitrogen would be present in the reaction. The majority of the exhaust gaseous species are CO2, H2O, N2, and in diesels excess O2 as well. In fact, these species constitute about 99% of the exhaust from an engine, leaving only 1 percent unaccounted for but made of mostly undesirable species.
Based on a measured average molecular mass of diesel fuel and its carbon to hydrogen ratio, one can calculate the average chemical formula for the diesel fuel. The following calculation is based on the molecular mass of diesel fuel of 191 (as determined by UOP Method 375-86 [Van Gerpen 2000]). Since the molecular mass of C is 12.0111 and that of hydrogen is 1.00797, the hydrocarbon designation of diesel fuel can be determined as follows:
(14)12.0111n + 1.00797m = 191
From actual fuel analysis each kg of diesel fuel contains 0.8616 kg of carbon or:
(15)0.8616 kg C / 12.0111 = 0.07173 kmol C
(16)0.1251 kg H / 1.00797 = 0.12411 kmol H
From Equations 15 and 16, the hydrogen to carbon ratio
(17)m/n = H/C = 0.12411 / 0.07173
By solving Equations 14 and 17, we can define diesel fuel as C13.883H24.053. Since diesel fuels are mixtures of hydrocarbons of variable composition, a certain variability of the above carbon and hydrogen designations will be seen in real life samples.
Stoichiometric Ratio in Diesel Combustion
Having determined the composition of diesel fuel it is relatively simple to calculate its stoichiometric ratio. By definition, the stoichiometric ratio is the ratio of air to fuel that when fully combusted would yield nothing but CO2, H2O, and N2. It is sometimes referred to as the chemically correct ratio. Applying this definition to the diesel fuel from the previous section yields the following:
(18)C13.883H24.053 + 94.744[0.21 O2 + 0.79 N2] + 13.883 CO2 + 12.026 H2O + 74.848 N2
From Equation 18, the molar A/F ratio is 94.744 kmol air/kmol fuel. On a mass basis the A/F ratio can be calculated as follows:
(19)[94.744 kmol air/kmol fuel] × [28.97 kg air/kmol air] × [kmol fuel/191 kg fuel] = 14.37 kg air/kg fuel
Additional Performance Parameters and Their Definition
After months and years designing an engine it must be put to the test of verifying whether or not all design assumptions and choices can indeed perform the intended output in an efficient manner. To fully appreciate what an engine can do the engineer must be well versed with the science of testing engines including laboratory tools designed for this purpose, evaluation and performance parameters, test methods, interpreting results, statistical tools, equipment calibration, and maintenance of test and analysis equipment. Of importance to the end user is the following:
The engine acquisition cost
The engine operating characteristics (output and speed)
The engine operating cost (fuel consumption and maintenance)
The engine reliability and its durability
The engine exhaust emission profile and the cost of making it environmentally friendly.
Of course, the importance of any of these items will depend on the specific application of the engine. Therefore, priorities have to be established before acquiring an engine to reflect the purpose for which the engine will be used. Nevertheless, there are common methods that are used to evaluate engine performance as well as their emission profiles. In this section, engine performance parameters, test tools, and test methodologies will be described and in some cases quantified.
Of primary importance to the designer, engine development engineer, end user, and others in the industry is the power output of an engine. The power output is defined by a maximum torque at a given engine speed. The engine maximum power output, sometimes referred to as rated power, is defined as follows:
(20)Power Output = (T × N) / Constant
where T is engine torque in lb-ft or N.m, and N is engine speed in rotations per minute. The appearance of torque in Equation 20 leads us to seek a more basic definition of power by considering the fundamental purpose for using an engine. An engine produces work that we can use in various applications, and power is the rate at which this work is produced. The most common method used to measure power is a device designed to brake the engine and is called a dynamometer. There are many types of dynamometers, but they have certain features in common. Most dynamometers are designed with a stator that does not rotate and is coupled electromagnetically to a rotor as shown in Figure 22. The rotor is the second major feature of a dynamometer and is concentric with the stator. It is also coupled to the engine and rotates around the same axis as the stator. In electromagnetic dynamometers, the rotor is driven by the engine and an electric field in the stator tries to oppose its motion. The electromagnetic force (F) exerted is measured by a load cell that is placed at distance (b) from the center of the load cell as shown in Figure 22. The product of the force (F) and distance (b) as expressed in Equation 21 defines torque.
(21)T = F × b
In one revolution the rotor travel a distance 2 r against resistance force f, thus its work for this one revolution is:
(22)Work = 2πrf
The rotor turning moment (rf) must be balanced exactly by the external turning moment that is the product (Fb) and this relationship can be expressed as follows:
(23)Rf = Fb
Substituting from Equation 23 into 22 we can then express work as:
(24)Work = 2πFb
Using the relationship of Equation 21 to express work per unit time gives the following:
(25)Work per minute = 2πTN
Since power is defined as the rate of doing work, we can then write the following:
(26)Work per minute = Power = 2πTN
Horsepower (hp) is a unit of power equal to 33,000 lb-ft per minute (550 lb-ft per second) in the English system, and the kilowatt (kW) is its equivalent in the metric system. The kilowatt is 550 × 0.746 = 738 lb-ft per second. Having defined these units, we can then express horsepower as:
(27)hp = 2πTN / 33,000 = T × N / 5252
Equation 27 establishes a relationship between power output, torque, and engine speed. From this relationship we conclude that since hp is a function of both torque and speed, then it is possible to design an engine to achieve power through high torque or through high speed. Engines designed for high torque output are usually large and built to withstand high internal forces. Their maximum speeds are quite low ranging from a few hundred revolutions per minute (rpm) to perhaps 1800 to 2100 rpm. Stationary engines are on the low end of the speed spectrum while on highway trucks and mid-range engines occupy the high end of the speed range. High torque/low speed engines are very suitable for heavy-truck applications enabling them to move extremely high loads away from loading docks or traffic lights at very low engine speeds. Meanwhile small high speed engines, such as those powering many passenger cars, produce their high power at very high engine speeds (above 5,000 rpm). An extreme example of these types of applications is the race car engine with speeds far exceeding 9,000 rpm.
The brake power, as discussed above, has been so named after the method used for its quantification. Brake power is a good measure for the useful power produced by the engine. Indicated power is that which is produced by the direct application of the gas pressure on the surface of the piston. By integrating cylinder pressure during a complete combustion cycle one can obtain an value for the cycle pressure that can be used to calculate indicated power.
From Figure 23 the net pressure applied to the surface of the piston is (Area A - Area B). Area A is bordered by the clockwise arrows and is regarded as positive pressure on the piston. This is a conventional way rather than a purely scientific way since during the compression stroke, it is the piston that is doing work on the gas. A similar consideration is given to Area B, where the piston is found once again to be pushing exhaust gases while it moves from BDC to TDC. Area B is often considered a measure for pumping losses. In addition to the Area B, friction losses are also subtracted from indicated pressure to obtain brake power. In other words:
(28)Indicated Power = Brake Power + Pumping Power + Friction Power
In turbocharged engines pumping losses are relatively small and can be neglected and resulting in the following relationship:
(29)Indicated Power = Brake Power + Friction Power
The term friction power in Equation 29 includes power required to expel exhaust gases, induct fresh air, overcome piston ring/liner friction, bearing friction, and drive engine accessories as well as account for parasitic losses elsewhere within the engine. It follows that mechanical efficiency (ηmech) can be defined as the ratio of useful power (brake power) over available power (indicated power). In mathematical form it can be expressed as follows:
(30)Mechanical Efficiency = (Brake Power) / (Indicated Power)
(31)ηmech = Pb/Pi = 1 - (Pf/Pi)
where Pi is indicated power, Pb is brake power, and Pf is friction power. Normally friction power losses increase with engine speed. An estimate of friction power can be obtained from normal engine brake power and fuel consumption basic relationship. An example is given in Figure 24 where regular engine dynamometer test information of brake horsepower and fuel consumption can be used at constant engine speed to derive an estimate of friction power. By plotting brake power on the X-axis and fuel consumption on the Y-axis, data from zero to 300 horsepower are represented by an almost straight line except for the high output points. As this line is extended to the left and intersects the X-axis it gives us an estimate of the friction power as shown in Figure 24. At the point where that line intersects the vertical line at zero power output, the fuel consumption required to overcome engine friction at that speed can be read (about 15 lb/hr in this case). The line describing engine brake power versus fuel consumption, its extension to the left, shown in dotted line, and the estimate of friction fuel consumption were attributed to an Englishman by the name of Willans, and hence the name given to this characteristic line.
Even though diesels are not usually throttled, operating them at high speed and requiring greater volume of air to be inducted into the cylinder through the narrow passage of an intake valve causes pumping losses to increase and volumetric efficiency to degrade. For this as well as other reasons, in modern engines valve area was increased by adopting two intake valves per cylinder instead of just one.
Indicated Mean Effective Pressure
Area A in Figure 23 was described as the area indicating the work exerted by the working fluid on the surface of the piston. Pressure resulting from the combustion process, as a function of the cylinder volume, is applied to the piston surface to produce power. The indicated mean effective pressure (imep) is the work exerted by the gas on the piston per unit swept volume. The following is an expression of imep:
(32)imep = ∫ (Pi/Vd) dV
Graphically, indicated mean effective pressure is illustrated in Figure 25.
Brake Mean Effective Pressure
While imep is a form of the bulk pressure exerted on the surface of the piston, brake mean effective pressure may be described as the portion of that imep that produces useful power. It represents the net work after subtracting friction, pumping, and other parasitic losses. The largest of these losses being that of friction as expressed by in Equation 29. There is a relation of proportionality between brake mean effective pressure (bmep) and engine torque. Rather than using torque which depends on engine size, bmep is preferred since it is a normalized parameter as given in Equation 33.
(33)bmep = ∫ (Pb/Vd) dV
Other useful relationships for bmep include those given in Equations 31 and 32. Numerically, bmep can be calculated using its proportional relationship to torque as shown in Equations 34 and 35 for two- and four-stroke engines, respectively.
(34)bmep = 75.4 × T / CID, psi
(35)bmep = 150.8 × T / CID, psi
where CID is the engine displacement in cubic inch. It is customary to compare engines on the basis of their bmep using their peak torque value. However, a more accurate comparison of engines should consider the entire bmep characteristic of engines versus their speed range.
Specific Fuel Consumption
Fuel consumption in mass per unit time is normally recorded during engine testing. One way to evaluate engine efficiency is to ratio fuel consumption to useful power. The result of this mathematical treatment produces the term brake specific fuel consumption (bsfc). In essence, bsfc is a measure of how much fuel an engine consumes in the process of producing an output of one horsepower (see Equation 36).
(36)bsfc = (Fuel Consumption per Unit Time) / (Brake Power Output), lb/bhp-hr
Single cylinder engines are popular in engine research work. Since power is produced by one cylinder only, friction and parasitic losses are disproportionately high relative to the power output of these engines. In these cases, rather than using the term bsfc engineers compute indicated specific fuel consumption (isfc). The term isfc is calculated on the basis of indicated power output as given in Equation 37.
(37)isfc = (Fuel Consumption per Unit Time) / (Indicated Power Output), lb/bhp-hr
Volumetric efficiency is a measure of the breathing quality of an engine. It is the ratio of the mass of air actually inducted by the engine during its intake stroke to the theoretical mass of air that could be inducted given the displacement of that engine. Equation 38 puts this relationship into a mathematical form.
(38)ηvol = (Actual Mass of Air Inducted) / (Theoretical Mass of Air to Fill Displacement)
Obert [Obert 1968] describes this definition as a misnomer because it is a ratio of two masses rather two volumes. Yet, it is the conventional way of calculating volumetric efficiency since it takes air density into consideration.
Engine Specific Weight and Volume
Total engine weight and volume are very important for packaging and cost considerations. For instance, under-hood space for many on highway as well as off road applications is very limited. Therefore, engines having the right power output and torque characteristics may have different volumes where the smallest volume would be of greatest advantage. Not only is engine volume very important, but also its weight. The lighter the weight the greater its advantage for a given application since it cost fuel to transport additional weight. The terms specific engine weight and specific engine volume are used to compare engines of similar power outputs, but having different size and weight. Equations 39 and 40 give the calculation for specific volume and specific weight, respectively.
(39)Specific Volume = (Engine Volume) / (Rated Power)
(40)Specific Weight = (Engine Weight) / (Rated Power)
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