EXAMPLE PROBLEM 3-3
The engine in Example Problems 3-1 and 3-2 is now run at part throttle such that the intake pressure is 50 kPa. Calculate the temperature in the cylinder at the start of the compression stroke.
The temperature of the intake air can be assumed to be the same even though it has experienced a pressure reduction expansion when passing the throttle valve. This is because it still flows through the same hot intake manifold after the throttle. However, the temperature of the exhaust residual will be reduced due to the expansion cooling it undergoes when the intake valve opens and the pressure in the cylinder drops to 50 kPa. The temperature of the exhaust residual after expansion can be approximated using Fig. 3-4 and the isentropic expansion model such that:
3-6 DIESEL CYCLE
Early CI engines injected fuel into the combustion chamber very late in the com- pression stroke, resulting in the indicator diagram shown in Fig. 3-7. Due to ignition delay and the finite time required to inject the fuel, combustion lasted into the expansion stroke. This kept the pressure at peak levels well past TDC. This com- bustion process is best approximated as a constant-pressure heat input in an air-standard cycle, resulting in the Diesel cycle shown in Fig. 3-8. The rest of the cycle is similar to the air-standard Otto cycle. The diesel cycle is sometimes called a Constant· Pressure cycle.
If reptesentative numbers are introduced into Eq. (3-73), it is found that the value of the term in brackets is greater than one. When this equation is compared with Eq. (3-31), it can be seen that for a given compression ratio the thermal effi- ciency of the Otto cycle would be greater than the thermal efficiency of the Diesel cycle. Constant-volume combustion at TDC is more efficient than constant-pressure combustion. However, it must be remembered that CI engines operate with much higher compression ratios than SI engines (12 to 24 versus 8 to 11) and thus have higher thermal efficiencies.
3-7 DUAL CYCLE
If Eqs. (3-31) and (3-73) are compared, it can be seen that to have the best of both worlds, an engine ideally would be compression ignition but would operate on the Otto cycle. Compression ignition would operate on the more efficient higher com- pression ratios, while constant-volume combustion of the Otto cycle would give higher efficiency for a given compression ratio.
The modern high-speed CI engine accomplishes this in part by a simple operating change from early diesel engines. Instead of injecting the fuel late in the compression stroke near TDC, as was done in early engines, modern CI engines start to inject the fuel much earlier in the cycle, somewhere around 20° bTDC. The first fuel then ignites late in the compression stroke, and some of the combustion occurs almost at constant volume at TDC, much like the Otto cycle. A typical indicator dia- gram for a modern CI engine is shown in Fig. 3-9. Peak pressure still remains high into
the expansion stroke due to the finite time required to inject the fuel. The last of the fuel is still being injected at TDC, and combustion of this fuel keeps the pressure high into the expansion stroke. The resulting cycle shown in Fig. 3-9 is a cross between an SI engine cycle and the early CI cycles. The air-standard cycle used to analyze this modern CI engine cycle is called aDual cycle, or sometimes aLimited Pressure cycle (Fig. 3-10). It is a dual cycle because the heat input process of combustion can best be approximated by a dual process of constant volume followed by constant pressure. It can also be considered a modified Otto cycle with a limited upper pressure.
Thermodynamic Analysis of Air-Standard Dual Cycle
The analysis of an air-standard Dual cycle is the same as that of the Diesel cycle except for the heat input process (combustion) 2-x-3.
3-8 COMPARISON OF OTTO, DIESEL, AND DUAL CYCLES
Figure 3-11 compares Otto, Diesel, and Dual cycles with the same inlet conditions and the same compression ratios. The thermal efficiency of each cycle can be written as:
TIt
=
1 - Iqout I/Iqin I (3-90)The area under the process lines on T-s coordinates is equal to the heat trans- fer, so in Fig. 3-11(b) the thermal efficiencies can be compared. For each cycle,qout
is the same (process 4-1).qin of each cycle is different, and using Fig. 3-11(b) and Eq.
(3-90) it is found for these conditions:
( TIt)OTIO
>
(TIt)DUAL>
(TIt)DIESEL (3-91)However, this is not the best way to compare these three cycles, because they do not operate on the same compression ratio. Compression ignition engines that operate on the Dual cycle or Diesel cycle have much higher compression ratios than do spark ignition engines operating on the Otto cycle. A more realistic way to com- pare these three cycles would be to have the same peak pressure-an actual design limitation in engines. This is done in Fig. 3-12. When this figure is compared with Eq. (3-90), it is found:
( TIt)DIESEL >(TIt)DUAL >(TIt )OTIO (3-92)
Comparing the ideas of Eqs. (3-91) and (3-92) would suggest that the most effi- cient engine would have combustion as close as possible to constant volume but would be compression ignition and operate at the higher compression ratios which that requires. This is an area where more research and development is needed.
EXAMPLE PROBLEM 3-4
A small truck has a four-cylinder, four-liter CI engine that operates on the air-standard Dual cycle (Fig. 3-10) using light diesel fuel at an air-fuel ratio of 18. The compression ratio of the engine is 16:1 and the cylinder bore diameter is 10.0 cm. At the start of the compression stroke, conditions in the cylinders are 60°C and 100 KPa with a 2%
exhaust residual. It can be assumed that half of the heat input from combustion is added at constant volume and half at constant pressure.
Calculate:
1. temperature and pressure at each state of the cycle
3-9 MILLER CYCLE
The Miller cycle, named after R. H. Miller (1890-1967), is a modern modification of the Atkinson cycle and has an expansion ratio greater than the compression ratio.
This is accomplished, however, in a much different way. Whereas an engine designed to operate on the Atkinson cycle needed a complicated mechanical linkage system of some kind, a Miller cycle engine uses unique valve timing to obtain the same desired results.
Air intake in a Miller cycle is unthrottled. The amount of air ingested into each cylinder is then controlled by closing the intake valve at the proper time, long before
Figure 3-14 Air-standard Miller cycle for unthrottled naturally aspirated four- stroke cycle SI engine. If the engine has early intake valve closing, the cycle will be 6-7-1-7-2-3-4-5-7-6. If the engine has late intake valve closing, the cycle will be 6-7- 5-7-2-3-4-5-7-6.
BDC (point 7 in Fig. 3-14). As the piston then continues towards BDC during the lat- ter part of the intake stroke, cylinder pressure is reduced along process 7-1. When the piston reaches BDC and starts back towards TDC cylinder pressure is again increased during process 1-7. The resulting cycle is 6-7-1-7-2-3-4-5-6. The work produced in the first part of the intake process 6-7 is canceled by part of the exhaust stroke 7-6, process 7-1 is canceled by process 1-7, and the net indicated work is the area within loop 7-2-3- 4-5-7. There is essentially no pump work. The compression ratio is:
rc
=
V7/V2 (3-93)and the larger expansion ratio is:
re =V4/V2 = V4/V3 (3-94)
The shorter compression stroke which absorbs work, combined with the longer expansion stroke which produces work, results in a greater net indicated work per cycle. In addition, by allowing air to flow through the intake system unthrottled, a major loss experienced by most SI engines is eliminated. This is espe- cially true at part throttle, when an Otto cycle engine would experience low pressure in the intake manifold and a corresponding high negative pump work. The Miller
Sec.3-9 Miller Cycle 105
cycle engine has essentially no pump work (ideally none), much like a CI engine.
This results in higher thermal efficiency.
The mechanical efficiency of a Miller cycle engine would be about the same as that of an Otto cycle engine, which has a similar mechanical linkage system. An Atkinson cycle engine, on the other hand, requires a much more complicated mechanical linkage system, resulting in lower mechanical efficiency.
Another variation of this cycle can be obtained if the intake air is unthrottled and the intake valve is closed after BDC. When this is done, air is ingested during the entire intake stroke, but some of it is then forced back into the intake manifold before the intake valve closes. This results in cycle 6-7-5-7-2-3-4-5-6 in Fig. 3-14. The net indicated work is again the area within loop 7-2-3-4-5-7, with the compression and expansion ratios given by Eqs. (3-93) and (3-94).
For either variation of the cycle to work efficiently, it is extremely important to be able to close the intake valve at the precise correct moment in the cycle (point 7).
However, this point where the intake valve must close changes as the engine speed and/or load is changed. This control was not possible until variable valve timing was perfected and introduced. Automobiles with Miller cycle engines were first mar- keted in the latter half of the 1990s. A typical value of the compression ratio is about 8:1, with an expansion ratio of about 10:1.
The first production automobile engines operating on Miller cycles used both early intake valve closing methods and late intake valve closing methods. Several types of variable valve timing systems have been tried and are being developed. At present, none of these offer full flexibility, and major improvements are still needed.
If the intake valve is closed bBDC, less than full displacement volume of the cylinder is available for air ingestion. If the intake valve is closed aBDC, the full dis- placement volume is filled with air, but some of it is expelled out again before the valve is closed (process 5-7 in Fig. 3-14). In either case, less air and fuel end up in the cylinder at the start of compression, resulting in low output per displacement and low indicated mean effective pressure. To counteract this, Miller cycle engines are usually supercharged or turbocharged with peak intake manifold pressures of 150-200 kPa. Fig. 3-15 shows a supercharged Miller engine cycle.
EXAMPLE PROBLEM 3-5
The four-cylinder,2.5-literSI automobile engine of Example Problem 3-1 is converted to operate on an air-standard Miller cyclewith early valve closing(cycle6-7-1-7-2-3-4- 5-6 in Fig. 3-15). It has a compression ratio of 8:1 and an expansion ratio of 10:1.A supercharger is added that gives a cylinder pressure of 160KPa when the intake valve closes,as shownin Fig. 3-15.The temperature is again 60°Cat this point. The same fuel and AF are used with combustion efficiency17c =100%.
Calculate:
1. temperature and pressure at all points in the cycle 2. indicated thermal efficiency
3. indicated mean effectivepressure 4. exhaust temperature
3-10 COMPARISON OF MILLER CYCLE AND OTTO CYCLE
When the Otto cycle engine of Example Problems 3-1 and 3-2 is compared with a similar engine operating on a Miller cycle as in Example Problem 3-5, the superior- ity of the Miller cycle can be seen. Table 3-1 gives such a comparison.
Temperatures in the two cycles are about the same, except for the exhaust temperature. It is important that the temperature at the beginning of combustion for either cycle be low enough so that self-ignition and knock do not become prob- lems. The lower exhaust temperature of the Miller cycle is the result of greater expansion cooling that occurs from the essentially same maximum cycle tempera- ture. Lower exhaust temperature means less energy is lost in the exhaust, with more of it used as work output in the longer expansion stroke. Pressures throughout the Miller cycle are higher than those of the Otto cycle, mainly because of the super- charged input. The output parameters of imep, thermal efficiency, and work are all higher for the Miller cycle, showing the technical superiority of this cycle. Some of the indicated work and indicated thermal efficiency of the Miller cycle will be lost due to the need to drive the supercharger. Even with this considered, however, brake work and brake thermal efficiency will be substantially greater than in an Otto cycle engine. If a turbocharger were used instead of a supercharger, brake out- put parameter values would be even higher. One cost of this higher output is the greater complexity of the valve system of the Miller cycle engine, and the corre- sponding higher manufacturing costs.
TABLE3-1 COMPARISON OF OTTO AND MILLER CYCLES
Miller Cycle Otto Cycle
Temperature at start of combustion Tz: 689 K 707 K
Pressure at start of combustionPz: 2650 kPa 1826 kPa
Maximum temperature T3: 3908 K 3915 K
Maximum pressureP3: 15,031kPa 10,111 kPa
Exhaust temperature: 1066 K 1183 K
Indicated net work per cylinder
per cycle for sameQin: 1.380 kJ 1.030 kJ
Indicated thermal efficiency: 56.6% 52.9%
Indicated mean effective pressure: 2208 kPa 1649 kPa
110 Engine Cycles Chap. 3
Process 3-4-5-intake, and exhaust scavenging.
Exhaust port open and intake port open:
Intake air entering at an absolute pressure on the order of 140-180 kPa fills and scavenges the cylinder. Scavenging is a process in which the air pushes out most of the remaining exhaust residual from the previous cycle through the open exhaust port into the exhaust system, which is at about one atmosphere pressure. The piston uncovers the intake port at point 3, reaches BDC at point 4, reverses direction, and again closes the intake port at point 5. In some engines fuel is mixed with the incom- ing air. In other engines the fuel is injected later, after the exhaust port is closed.
Many compression ignition engines-especially large ones-operate on two-stroke cycles. These cycles can be approximated by the air-standard cycle shown in Fig.
3-17. This cycle is the same as the two-stroke SI cycle except for the fuel input and combustion process. Instead of adding fuel to the intake air or early in the compres- sion process, fuel is added with injectors late in the compression process, the same as with four-stroke cycle CI engines. Heat input or combustion can be approximated by a two-step (dual) process .
•
around since 1816, and while it is not a true internal combustion engine, it is included here briefly because it is a heat engine used to propel vehicles as one of its applications. The basic engine uses a free-floating, double-acting piston with a gas chamber on both ends of the cylinder. Combustion does not occur within the cylin- der, but the working gas is heated with an external combustion process. Heat input can also come from solar or nuclear sources. Engine output is usually a rotating shaft [8].
A Stirling engine has an internal regeneration process using a heat exchanger.
Ideally, the heat exchanger uses the rejected heat in process 4-1 to preheat the internal working fluid in the heat addition process 2-3. The only heat transfers with the surroundings then occur with a heat addition process 3-4 at one maximum tem- perature Thigh,and a heat rejection process 1-2 at one minimum temperature Tlow. If the processes in the air-standard cycle in Fig. 3-18 can be considered reversible, the thermal efficiency of the cycle will be:
(1Jt)sTIRLING = 1 - (Tlow/Thigh) (3-116)
This is the same thermal efficiency as a Carnot cycle and is the theoretical maximum possible. Although a real engine cannot operate reversibly, a well- designed Stirling engine can have a very high thermal efficiency. This is one of the attractions which is generating interest in this type of engine. Other attractions include low emissions with no catalytic converter and the flexibility of many possible
Sec. 3-13 Lenoir Cycle 113
fuels that can be used. This is because heat input is from a continuous steady-state combustion in an external chamber at a relatively low temperature around 1000 K.
Fuels used have included gasoline, diesel fuel, jet fuel, alcohol, and natural gas. In some engines, the fuel can be changed with no adjustments needed.
Problems with Stirling engines include sealing, warm-up time needed, and high cost. Other possible applications include refrigeration, stationary power, and heat- ing of buildings.
HISTORIC-LENOIR ENGINE
One ofthe first successful engines developed during the second half of the 1800s was the Lenoir engine (Fig. 3-19). Several hundred of these were built in the 1860s. They operated on a two-stroke cycle and had mechanical efficiencies up to 5% and power output up to 4.5 kW (6 hp).
The engines were double acting, with combustion occurring on both ends of the piston. This gave two power strokes per revolution from a single cylinder [29].
3-13 LENOIR CYCLE
The Lenoir cycle is approximated by the air-standard cycle shown in Fig. 3-20. The first half of the first stroke was intake, with air-fuel entering the cylinder at atmos-
pheric pressure (process 1-2 in Fig. 3-20). At about halfway through the first stroke, the intake valve was closed and the air-fuel mixture was ignited without any com- pression. Combustion raised the temperature and pressure in the cylinder almost at constant volume in the slow-moving engine (process 2-3). The second half of the first stroke then became the power or expansion process 3-4. Near BDC, the exhaust valve opened and blowdown occurred (4-5). This was followed by the exhaust stroke 5-1, completing the two-stroke cycle. There was essentially no clearance volume.
Thermodynamic Analysis of Air-Standard lenoir Cycle
The intake process 1-2 and the latter half of the exhaust stroke process 2-1 cancel each other thermodynamically on P-V coordinates and can be left out of the analy- sis of the Lenoir cycle. The cycle then becomes 2-3-4-5-2.
3-14 SUMMARY
This chapter reviewed the basic cycles used in internal combustion engines.
Although many engine cycles have been developed, for over a century most auto- mobile engines have operated on the basic SI four-stroke cycle developed in the 1870s by Otto and others. This can be approximated and analyzed using the ideal air-standard Otto cycle. Many small SI engines operate on a two-stroke cycle, some- times (erroneously) called a two-stroke Otto cycle.
Early four-stroke CI engines operated on a cycle that can be approximated by the air-standard Diesel cycle. This cycle was improved in modern CI engines of the type used in automobiles and trucks. Changing the injection timing resulted in a
116 Engine Cycles Chap. 3
more efficient engine operating on a cycle best approximated by an air-standard Dual cycle. Most small CI engines and very large CI engines operate on a two-stroke cycle.
At present, most automobile engines operate on the four-stroke Otto cycle, but major research and development is resulting in two additional cycles for modem vehicles. Several companies have done major development work to try to create an automobile engine that would operate on an SI two-stroke cycle. Throughout his- tory, two-stroke cycle automobile engines have periodically appeared with varying success. These offer greater power per unit weight, but none would pass modem emission standards. Recent development has concentrated on producing an engine that would satisfy pollution laws. The major technological change is the input of fuel by injection directly into the combustion chamber after exhaust and air intake are completed. If this development work is successful, there will be automobiles on the market with two-stroke cycle engines.
Advances in valve timing technology, including variable timing, have led to the introduction of Miller cycle engines. The Miller cycle improves on the four-stroke SI Otto cycle by closing the intake valve at a more opportune time, either early or late.
This results in an expansion ratio that is greater than the compression ratio and rep- resents the most modem of engine cycles.
PROBLEMS
3-1. Cylinder conditions at the start of compression in an SI engine operating at WOT on an air-standard Otto cycle are 60°C and 98 kPa. The engine has a compression ratio of 9.5:1 and uses gasoline with AF =15.5. Combustion efficiency is 96%, and it can be assumed that there is no exhaust residual.
Calculate: (a) Temperature at all states in the cycle.[0C]
(b) Pressure at all states in the cycle. [kpa]
(c) Specific work done during power stroke. [kJ/kg]
(d) Heat added during combustion. [kJ/kg]
(e) Net specific work done. [kJ/kg]
(£) Indicated thermal efficiency. [%]
3.2. The engine in Problem 3-1 is a three-liter V6 engine operating at 2400 RPM. At this speed the mechanical efficiency is 84% .
Calculate: (a) Brake power. [kW]
(b) Torque. [N-m]
(c) Brake mean effective pressure. [kPa]
(d) Friction power lost. [kW]
(e) Brake specific fuel consumption. [gm/kW-hr]
(£) Volumetric efficiency. [%]
(g) Output per displacement. [kW/L]
Chap. 3 Problems 117
3-3. The exhaust pressure of the engine in Problem 3-2 is 100 kPa.
Calculate: (a) Exhaust temperature. [0C]
(b) Actual exhaust residual. [%]
(c) Temperature of air entering cylinders from intake manifold. [0C]
3-4. The engine of Problems 3-2 and 3-3 is operated at part throttle with intake pressure of 75 kPa. Intake manifold temperature, mechanical efficiency, exhaust residual, and air-fuel ratio all remain the same.
Calculate: (a) Temperature in cylinder at start of compression stroke. [0C]
(b) Temperature in cylinder at start of combustion. [0C]
3-5. An SI engine operating at WOT on a four-stroke air-standard cycle has cylinder condi- tions at the start of compression of 100°F and 14.7 psia. Compression ratio isrc = 10, and the heat added during combustion isqin =800 BTU/lbm. During compression the temperature range is such that a value for the ratio of specific heats k = 1.4 would be correct. During the power stroke the temperature range is such that a value ofk = 1.3 would be correct. Use these values for compression and expansion, respectively, when analyzing the cycle. Use a value for specific heat ofCv=0.216 BTU/lbm-oR, which best corresponds to the temperature range during combustion.
Calculate: (a) Temperature at all states in cycle. [OF]
(b) Pressure at all states in cycle. [psia]
(c) Average value ofkwhich would give the same indicated thermal effi- ciency value as the analysis in parts (a) and (b).
3-6. A CI engine operating on the air-standard Diesel cycle has cylinder conditions at the start of compression of 65°C and 130 kPa. Light diesel fuel is used at an equivalence ratio ofif>=0.8 with a combustion efficiency Tic=0.98. Compression ratio isrc = 19.
Calculate: (a) Temperature at each state of the cycle. [0C]
(b) Pressure at each state of the cycle. [kPa]
(c) Cutoff ratio.
(d) Indicated thermal efficiency. [%]
(e) Heat lost in exhaust. [kJ/kg]
3·7. A compression ignition engine for a small truck is to operate on an air-standard Dual cycle with a compression ratio of rc = 18. Due to structural limitations, maximum allowable pressure in the cycle will be 9000 kPa. Light diesel fuel is used at a fuel-air ratio of FA =0.054. Combustion efficiency can be considered 100%. Cylinder condi- tions at the start of compression are 50°C and 98 kPa.
Calculate: (a) Maximum indicated thermal efficiency possible with these conditions.
[%]
(b) Peak cycle temperature under conditions of part (a). [0C]
(c) Minimum indicated thermal efficiency possible with these conditions.
[%]
(d) Peak cycle temperature under conditions of part (c). [0C]
3-8. An in-line six, 3.3-liter CI engine using light diesel fuel at an air-fuel ratio of AF =20 operates on an air-standard Dual cycle. Half the fuel can be considered burned at con- stant volume, and half at constant pressure with combustion efficiency Tic = 100%.
Cylinder conditions at the start of compression are 60°C and 101 kPa. Compression ratio rc =14:1.
118 Engine Cycles Chap. 3
Calculate: (a) Temperature at each state of the cycle. [K]
(b) Pressure at each state of the cycle. [kPa]
(c) Cutoff ratio.
(d) Pressure ratio.
(e) Indicated thermal efficiency. [%]
(f) Heat added during combustion. [kJ/kg]
(g) Net indicated work. [kJ/kg]
3-9. The engine in Problem 3-8 produces 57 kW of brake power at 2000 RPM.
Calculate: (a) Torque. [N-m]
(b) Mechanical efficiency. [%]
(c) Brake mean effective pressure. [kPa]
(d) Indicated specific fuel consumption. [gmlkW-hr]
3-10. An Otto cycle SI engine with a compression ratio ofrc =9 has peak cycle temperature and pressure of 2800 K and 9000 kPa. Cylinder pressure when the exhaust valve opens is 460 kPa, and exhaust manifold pressure is 100 kPa.
Calculate: (a) Exhaust temperature during exhaust stroke. [0C]
(b) Exhaust residual after each cycle. [%]
(c) Velocity out of the exhaust valve when the valve first opens. [mlsec]
(d) Theoretical momentary maximum temperature in the exhaust. [0C]
3-11. An SI engine operates on an air-standard four-stroke Otto cycle with turbocharging.
Air-fuel enters the cylinders at 70°C and 140 kPa, and heat in by combustion equals
qin = 1800 kJ/kg. Compression ratio rc = 8 and exhaust pressure Fex = 100 kPa.
Calculate: (a) Temperature at each state of the cycle. [0C]
(b) Pressure at each state of the cycle. [kPa]
(c) Work produced during expansion stroke. [kJ/kg]
(d) Work of compression stroke. [kJ/kg]
(e) Net pumping work. [kJ/kg]
(f) Indicated thermal efficiency. [%]
(g) Compare with Problems 3-12 and 3-13.
3-12. An SI engine operates on an air-standard four-stroke Miller cycle with turbocharging.
The intake valves close late, resulting in cycle 6-7-8-7-2-3-4-5-6 in Fig. 3-15. Air-fuel enters the cylinders at 70°C and 140 kPa, and heat in by combustion equals qin =1800 kJ/kg. Compression ratio rc = 8, expansion ratio re = 10, and exhaust pressure Fex = 100 kPa.
Calculate: (a) Temperature at each state of the cycle. [0C]
(b) Pressure at each state of the cycle. [kPa]
(c) Work produced during expansion stroke. [kJ/kg]
(d) Work of compression stroke. [kJ/kg]
(e) Net pumping work. [kJ/kg]
(f) Indicated thermal efficiency. [%]
(g) Compare with Problems 3-11 and 3-13.
3-13. An SI engine operates on an air-standard four-stroke Miller cycle with turbocharging.
The intake valves close early, resulting in cycle 6-7-1-7-2-3-4-5-6 in Fig. 3-15. Air-fuel enters the cylinders at 70°C and 140 kPa, and heat in by combustion equals qin =1800
Chap. 3 Problems 119
kJ/kg. Compression ratio rc =8, expansion ratio re =10, and exhaust pressure Pex =
100 kPa.
Calculate: (a)Temperature at each state of the cycle. [0C]
(b) Pressure at each state of the cycle. [kPa]
(c) Work produced during expansion stroke. [kJ/kg]
(d) Work of compression stroke. [kJ/kg]
(e) Net pumping work. [kJ/kg]
(I) Indicated thermal efficiency. [%]
(g) Compare with Problems 3-11 and 3-12.
3-14. A six cylinder, two-stroke cycle CI ship engine with bore B =35 cm and stroke S= 105 cm produces 3600 kW of brake power at 210 RPM.
Calculate: (a) Torque at this speed. [kN-m]
(b) Total displacement. [L]
(c) Brake mean effective pressure. [kPa]
(d)Average piston speed. [mlsec]
3-15. A single-cylinder, two-stroke cycle model airplane engine with a 7.54-cm3displacement produces 1.42 kW of brake power at 23,000 RPM using glow plug ignition. The square engine (bore =stroke) uses 31.7 gmlmin of castor oil-methanol-nitromethane fuel at an air-fuel ratio AF =4.5. During intake scavenging, 65% of the incoming air-fuel mixture gets trapped in the cylinder, while 35% of it is lost with the exhaust before the exhaust port closes. Combustion efficiency 'TIc =0.94.
Calculate: (a) Brake specific fuel consumption. [gm/kW-hr]
(b) Average piston speed. [mlsec]
(c) Unburned fuel exhausted to atmosphere. [gm/min]
(d) Torque. [N-m]
3-16. A historic single-cylinder engine with a mechanical efficiency 'TIm =5% operates at 140 RPM on the Lenoir cycle shown in Fig. 3-20. The cylinder has a double acting piston with a 12-in. bore and a 36-in. stroke. The fuel has a heating value QLHV = 12,000 BTU/lbm and is used at an air-fuel ratio AF =18. Combustion occurs at constant vol- ume half way through the intake-power stroke when cylinder conditions equal 70°F and 14.7 psia.
Calculate: (a) Temperature at each state of cycle. [OF]
(b) Pressure at each state of cycle. [psia]
(c) Indicated thermal efficiency. [%]
(d) Brake power. [hp]
(e) Average piston speed. [ft/sec]
3-17. Cylinder conditions at the start of compression of a four-stroke cycle SI engine are 27°C and 100 kPa. The engine has a compression ratio ofrc =8:1, and heat addition from combustion isqin =2000 kJ/kg.
Calculate: (a) Temperature and pressure at each state of the cycle, using air-standard Otto cycle analysis with constant specific heats. [OC,kPa]
(b) Indicated thermal efficiency in part (a). [%]
(c) Temperature and pressure at each state of the cycle, using any stan- dard air tables which are based on variable specific heats as functions of temperature (e.g., reference [73]). [OC,kPa]
(d) Indicated thermal efficiency in part (c). [%]
120 Engine Cycles Chap. 3 DESIGN PROBLEMS
3-1D. Design an SI engine to operate on a six-stroke cycle. The first four strokes of the cycle are the same as a four-stroke Otto cycle. This is followed with an additional air-only intake stroke and an air-only exhaust stroke. Draw simple schematics, and explain the speed and operation of the camshafts when the valves open and close. Also, explain the control of the ignition process.
3·2D. Design a mechanical linkage system for a four-stroke cycle, reciprocating SI engine to operate on the Atkinson cycle (i.e., normal compression stroke and a power stroke which expands until cylinder pressure equals ambient pressure). Explain using simple schematic drawings.
3-3D. An SI engine operating on an four-stroke air-standard cycle using stoichiometric gaso- line is to have a maximum cylinder pressure of 11,000 kPa at WOT. Inlet pressure can be 100 kPa without supercharging, or it can be as high as 150 kPa with a supercharger.
Pick a compression ratio and inlet pressure combination to give maximum indicated thermal efficiency. Pick a compression ratio and inlet pressure to give maximum imep.
