# Internal Combustion Engine

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1 Internal Combustion Engine 1. A 9-cylinder, 4-stroke cycle, radial SI engine operates at 900rpm. Calculate: (1) How often ignition occurs, in degrees of engine rev. (2) How many power strokes per rev. (3) How many power strokes per sec. 2. Please draw the graph for HC, CO and NOx v.s. air-to-fuel ratio and make an explanation. 3. Please explain the variation of piston speed and piston-cylinder friction force of a 4-stroke engine while piston moving from TDC to BDC. Which stroke has the largest friction force? Why? 4. (1)Please explain the differences of the combustion of SI and CI engines; and (2) the causes of the formation of HC, CO and NOx in SI and CI engines respectively. 5. Please explain the positive and negative effects of the cooling system on engines. 6. A 6-cylinder, 4-stroke engine operates at an engine speed of 3500rpm. The bore and stroke of the engine are 90mm and 88mm respectively, and CR is 11, volumetric efficiency is 90%, AF=13. Calculate (1) actual intake air flow rate (kg/s); (2) fuel consumption rate (kg/s). (Ideal gas constant R=0.287kJ/kg-K) 7. A 6-cylinder engine with 3.6 liter swept volume operates on a 4-stroke cycle. It is connected to a dynamometer which gives a brake output torque reading of 230 N-m at 3600 rpm. The mechanical efficiency of the engine is 85%. Calculate (1) bmep (kpa); (2) imep (kpa); (3) brake power (kw); (4) indicated power (kw); (5) friction power (kw). 8. A single cylinder engine with 0.25 liter swept volume and CR=10, operates on a 4-stroke cycle. It is connected to a dynamometer which gives a brake output torque reading of 15 N-m at 6000 rpm. The A/F=13, and mechanical efficiency of the engine is 98%. At the start of compression, the cylinder gas pressure is 100kPa, and temperature is 40. Calculate (1) air consumption rate (kg/h); (2) fuel consumption rate (kg/h); (3) brake thermal efficiency; (4) bsfc (kg/kw-h). (Ideal gas constant, R=0.287kJ/kg-K, Q LHV =43000kJ/kg) 9. A 6-cylinder engine with 3.0 liter swept volume operates on a 4-stroke cycle at

2 4500rpm. The clearance volume of the square engine (B=S) is 56cc. Calculate (1) compression ratio; (2) bore and stroke (cm); (3) average piston speed (m/sec). 10. A 6-cylinder engine with 3.0 liter swept volume operates on a 4-stroke cycle at 4500rpm. The clearance volume is 56cc, and B=0.95S. Calculate (1) compression ratio; (2) bore and stroke (cm); (3) average piston speed (m/sec). 11. The following is the equation for piston displacement calculation, r x = r(1 cos θ ) + (1 cos 2 θ ) 4λ r=50mm, L=165mm, engine speed N=6500rpm. Calculate (1) piston speed at 15deg-ATDC; (2) piston speed at 15deg-BBDC and (3) the maximum piston speed (m/s) (λis the ratio of L to r). 12. A 4-cylinder engine operates on air-standard Otto cycle with 2.5 liter swept volume, CR=9, A/F=15. The initial condition before compression is P 1 =100kPa T 1 =60 o C. Calculate (1) the pressure and temperature of air in cylinder at the end of compression stroke; (2) compression work; (3) the pressure and temperature of air in cylinder at the end of combustion process; (4) cycle thermal efficiency. (Q LHV =44000kJ/kg, R=0.287kJ/kg-K, c v =0.821kJ/kg-K). 13. A 8-cylinder engine operates on air-standard Diesel cycle with 4.8 liter swept volume, CR=20, A/F=16. The initial condition before compression is P 1 =120kPa T 1 =50 o C. The combustion efficiency is 95%. Calculate (1) the pressure and temperature of air in cylinder at the end of compression stroke; (2) the maximum pressure and temperature of air in cylinder of the cycle; (3) cut-off ratio ( 截斷比 ) (R=0.287kJ/kg-K, c v =0.821kJ/kg-K, Q LHV =43000kJ/kg). 14. A 6-cylinder engine operates on air-standard CI Dual cycle with 3.6 liter swept volume, CR=20, A/F=16. The initial condition at the start of compression is P 1 =98kPa T 1 =50 o C. The combustion efficiency is 95%. If 30% fuel is burnt in constant volume, and 70% is burnt in constant pressure process. Calculate (1) the pressure and temperature of air in cylinder at the end of compression stroke; (2) compression work; (3) the maximum pressure and temperature of air in cylinder of the cycle (R=0.287kJ/kg-K, c v =0.821kJ/kg-K, Q LHV =43000kJ/kg). 15. An air-standard CI Dual cycle engine is designed as CR=18, and operates with A/F=15. The initial condition at the start of compression is P 1 =99kPa, T 1 =50 o C.

3 The combustion efficiency is 100%. The maximum allowable pressure in the cycle is 9000kPa. Calculate (1) the pressure and temperature of air in cylinder at the end of compression stroke; (2) the maximum temperature of air in cylinder of the cycle; (3) pressure ratio; (4) cut-off ratio ( 截斷比 ) (R=0.287kJ/kg-K, c v =0.821kJ/kg-K,Q LHV =43000kJ/kg). 16. If cycle thermal efficiency of an air-standard Diesel cycle engine is η=1-(t 4 -T 1 )/[k(t 3 -T 2 )]. Please use compression ratio (CR), cut-off ratio (α) and the ratio of specific heat capacity (k) to substitute the temperature ratio. 17. Compare thermal efficiency of Otto, Diesel and Dual cycles based on: (1) the same compression ratio, and (2) the same maximum pressure.(by using P-V or T-S diagram). 18. A 6-cylinder engine operates on air-standard CI Dual cycle with 3.6 liter swept volume, CR=20, A/F=16. The initial condition at the start of compression is P 1 =98kPa, T 1 =50 o C. The combustion efficiency is 95%. The input energy per cylinder for each cycle is 1.975kJ, where 60% fuel is burnt in constant volume, and 40% in constant pressure process. Calculate (1) the pressure and temperature of air in cylinder at the end of compression stroke; (2) the maximum pressure and temperature of air in cylinder in the cycle; (3) the cylinder volume at the end of combustion process (R=0.287kJ/kg-K, c v =0.821kJ/kg-K, Q LHV =43000kJ/kg). 19. A four-cylinder, two-stroke cycle diesel engine with 10.9-cm bore and 12.6-cn stroke produces 88 kw of brake power at 2000rpm. Compression ratio CR=18. Calculate: (1) engine displacement [cm 3 ]; (2) clearance volume of one cylinder [cm 3 ]; (3) torque (N-m); (4) bmep [kpa]. 20. A 4-cylinder, 2.4 liter engine operates on a 4-stroke cycle at 3200rpm. The compression ratio is 9.4, the connecting rod length L=18cm, and the bore and stroke are related as S=1.06B. Calculate (1) clearance volume of one cylinder [cm 3 ]; (2) bore and stroke [cm]; (3) average piston speed [m/sec]. 21. A 5-cylinder, 3.5-liter SI engine operates on a 4-stroke cycle at 2500rpm. At this condition, the mechanical efficiency of engine is 62% and 1000J of indicated work are produced each cycle in each cylinder. Calculate (1) imep [kpa]; (2) bmep [kpa]; (3) fmep [kpa]; (4) brake power [kw]; (5) torque[n-m]. 22. A small single-cylinder, two-stroke SI engine operates at 8000rpm with a

4 volumetric efficiency of 85%. The engine is square (bore=stroke) and has a displacement of 6.28 cm 3. The fuel-air ratio FA= Calculate (1) average piston speed [m/sec]; (2) air flow rate into engine [kg/sec]; (3) fuel flow rate into engine [kg/sec]; (4) fuel input for one cycle [kg/cycle]. 23. A 3.1-liter, 4-cylinder, 2-stroke SI engine is mounted on an electric generator dynamometer. When the engine is running at 1200rpm, output from the 220-V DC generator is 54.2 amps. The generator has an mechanical efficiency of 87%. Calculate (1) power output of the engine [kw]; (2) engine torque [N-m]; (3) engine bmep [kpa] 24. An SI, 6-liter, V8 race car engine operates at WOT on a 4-stroke cycle at 6000rpm, using Stoichiometric nitromethane(a/f=1.7, Q LHV =10920kJ/kg). Fuel enters the engine at a rate of 0.198kg/sec and combustion efficiency is 99%. Calculate (1) volumetric efficiency of engine [%]; (2) flow rate of air into the engine [kg/sec]; (3) heat added per cycle per cylinder [kj]; (4) chemical energy from unburned fuel in the exhaust [kw]. 25. Cylinder conditions at the start of compression in an SI engine at WOT on an air-standard Otto cycle are 60 and 98kpa. 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 (1) temperature and pressure at the end of compression [, kpa]; (2) temperature and pressure at the end of combustion [, kpa]; (3) indicated thermal efficiency [%]. (R=0.287kJ/kg-K, c v =0.821kJ/kg-K, Q LHV =43000kJ/kg) 26. A 3-liter V6 engine, cylinder conditions at the start of compression in an SI engine at WOT and 2400 rpm on an air-standard Otto cycle are 60 and 98kpa. The work per cylinder per cycle is 0.78 kj. The engine has a compression ratio of 9.5:1 and uses gasoline with AF=15.5. Combustion efficiency is 96%, and mechanical efficiency is 84%. It can be assumed that there is no exhaust residual. Calculate (1) brake power [kw]; (2) torque [N-m]; (3) brake mean effective pressure [kpa]; (4) brake specific fuel consumption [kg/kw-h]. (5) Output power per displacement [kw/l]. (R=0.287kJ/kg-K, c v =0.821kJ/kg-K, Q LHV =43000kJ/kg) 27. A CI engine operating on the air-standard Diesel cycle has cylinder conditions at the start of compression of 65 and 135kpa. Light diesel fuel is used at an equivalence ratio of φ=0.8 with a combustion efficiency of η c =0.98. Compression

5 ratio is CR=19 Calculate (1) temperatures at the end of compression and combustion [ ]; (2) pressures at the end of compression and combustion [kpa]; (3) cut-off ratio. (Q LHV =42500kJ/kg) 28. A compression ignition engine for a small truck is to operate on an air-standard Dual cycle with a compression ratio of CR=18. Due to structural limitations, maximum allowable pressure in the cycle will be 9000kPa. Light diesel fuel is used at a fuel-air ratio of FA= Combustion efficiency can be considered 100%. Cylinder conditions at the start of compression are 50 and 98kpa. Calculate (1) max. indicated thermal efficiency possible with these conditions[%]; (2) peak cycle temperature under conditions of part (1). (R=0.287kJ/kg-K, c v =0.821kJ/kg-K, Q LHV =42500kJ/kg) 29. A compression ignition engine for a small truck is to operate on an air-standard Dual cycle with a compression ratio of CR=18. Due to structural limitations, maximum allowable pressure in the cycle will be 9000kPa. Light diesel fuel is used at a fuel-air ratio of FA= Combustion efficiency can be considered 100%. Cylinder conditions at the start of compression are 50 and 98kpa. Calculate (1) min. indicated thermal efficiency possible with these conditions[%]; (2) peak cycle temperature under conditions of part (1). (R=0.287kJ/kg-K, c v =0.821kJ/kg-K, Q LHV =42500kJ/kg) 30. 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 is burnt at constant volume, and half at constant pressure with combustion efficiency η c =100%. Cylinder conditions at the start of compression are 60 and 101 kpa. Compression ratio is 14:1. Calculate (1) temperatures and pressure at the end of compression [, kpa]; (2) heat added during combustion [kj/kg]; (3) temperatures and pressures at the end of combustion [, kpa]; (4) cut-off ratio; (5) pressure ratio;. (R=0.287kJ/kg-K, c v =0.821kJ/kg-K, Q LHV =42500kJ/kg) 31. A single-cylinder, 4-stroke CI engine with 12.9-cn bore and 18.0-cm stroke, operating at 800rpm, uses kg of fuel in four minutes while developing a torque of 76 N-m. Calculate (1) brake power [kw]; (2) brake specific fuel consumption [kg/kw-h]; (3) brake mean effective pressure; (4) output power per displacement [kw/l]. 32. (1) Higher heating value of methane is 55.5MJ/kg. Calculate its lower heating

6 value [MJ/kg]; (2) higher heating value of CO is 10.1MJ/kg. Calculate its lower heating value [MJ/kg](latent heat of water = kJ/kg). 33. Isooctane is burnt with air in an equivalence ratio of Assuming complete combustion, derive (1) the balanced chemical reaction equation; (2) air-fuel ratio; (3) how much excess air is used [%]; (4) AKI (anti-knock index) and FS (fuel sensitivity). 34. Methane is burned with air. Dry analysis of the exhaust gives the following volume percents: CO 2 =10%, CO=0.9%, O 2 =1.85%, with the rest being N 2. Derive (1) the balanced chemical reaction equation; (2) actual air-fuel ratio, (A/F) act ; (3) Stoichiometric air-fuel ratio, (A/F) stoi, (4) equivalence ratio; (5) if fuel consumption is 5kg/h, derive CO 2 emission [kg/h]. 35. An engine is fuelled with the mass ratio of 90%-C 8 H 18 and 10%-CH 3 OH. The fuel is combusted with air. Derive (1) the balanced chemical reaction equation; (2) Stoichiometric air-fuel ratio, (A/F) stoi. 36. The mass composition of fuel is 86.5%-C, 13.3%-H and unburned material of 0.2%. Calculate (1) Stoichiometric air-fuel ratio, (A/F) stoi ; (2) if dry analysis of the exhaust gives the following volume percents: CO 2 =12.1%, O 2 =4.4%, N 2 =83.5%. Calculate actual air-fuel ratio, (A/F) act, and (3) the molar fraction in wet analysis. 37. An SI engine is fuelled with ethanol (C 2 H 5 OH), and operates at 150% Stoichiometric air. Derive (1) the balanced chemical reaction equation; (2) air-fuel ratio; (3) equivalence ratio. 38. An SI engine is fuelled with isooctane (C 8 H 18 ), and combusted with 120% Stoichiometric dry air. If the exhaust pressure is 100kPa, calculate the exhaust temperature when water will start to condense (Table to be attached). Table of saturated temperature and pressure of water T( ) P (kpa)

7 39. C 4 H 8 is burned in an engine with a fuel-rich air-fuel ratio. Dry analysis of the exhaust gives the following volume percents: CO 2 =14.95%, C 4 H 8 =0.75%, O 2 =0%, with the rest being N 2. Higher heating value of this fuel is Q HHV =46.9MJ/kg. Calculate (1) air-fuel ratio; (2) equivalence ratio; (3) lower heating value of fuel [MJ/kg]; (4) energy released when one kg of this fuel is burned in the engine with a combustion efficiency of 98%[MJ].(latent heat of water=2442.3kj/kg) 40. Hydrogen is used as a fuel in an SI engine, and burned with Stoichiometric oxygen. Reactants enter at a temperature 25 and complete combustion occurs at constant pressure. The exhaust pressure is 101 kpa. Write the balanced chemical reaction equation. Calculate (1) fuel-oxygen ratio; (2) equivalence ratio; (3) due point temperature of exhaust (Table to be attached). Table of saturated temperature and pressure of water T( ) P (kpa)

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