IC Engines and Compressors

What to remember

• A four-stroke engine completes its cycle in two crankshaft revolutions (suction, compression, power, exhaust); a two-stroke engine in one revolution. SI engines run on the Otto cycle with spark ignition; CI engines on the Diesel cycle with compression ignition.
• Indicated power IP = p_m L A n_c N_c / 60 (N_c = N/2 for four-stroke). Brake power BP = 2πNT/60. Mechanical efficiency = BP/IP.
• Single-stage compressor work is least for isothermal compression. Multistage compression with intercooling needs equal pressure ratio per stage: intermediate pressure p_i = √(p₁p₂) for two stages.

1. Engine terms

• Bore D: cylinder diameter. Stroke L: piston travel between top dead centre (TDC) and bottom dead centre (BDC).
• Swept volume V_s = (π/4) D² L. Clearance volume V_c: volume above the piston at TDC.
• Compression ratio r = (V_s + V_c)/V_c. Example: V_s = 500 cc and V_c = 50 cc give r = 11.
• Typical compression ratios: SI about 6 to 11; CI about 14 to 22.
• Piston speed (mean) = 2LN/60.

2. Four-stroke and two-stroke engines

• Valve timing: the inlet valve opens slightly before TDC and closes after BDC; the exhaust valve opens before BDC and closes after TDC. The period when both are open is valve overlap.
• Camshaft rotates at half the crankshaft speed in a four-stroke engine.
• Firing order of a four-cylinder engine is commonly 1-3-4-2 or 1-2-4-3.

3. SI and CI engines

• Knock in SI engines: auto-ignition of the end gas ahead of the flame front. Rating: octane number (iso-octane = 100, n-heptane = 0). Tetra-ethyl lead was an anti-knock additive and is now banned.
• Knock in CI engines: caused by long ignition delay and sudden burning of accumulated fuel. Rating: cetane number (cetane = 100, alpha-methyl naphthalene = 0). Higher cetane means shorter delay.
• Factors to reduce SI knock: lower compression ratio, higher octane fuel, shorter flame path, turbulence, cooler charge. To reduce CI knock: higher compression ratio, higher cetane, higher intake temperature.
• Stoichiometric air-fuel ratio for petrol is about 15:1 by mass. Rich mixture gives more power; lean mixture gives better economy.
• Carburettor: float chamber, main jet, venturi, throttle valve. Direct and multi-point injection are modern methods.
• Ignition systems: battery (coil) or magneto. Diesel engines use a fuel pump, injector and governor.
• Cooling: air cooling (fins) or water cooling (pump and radiator). Lubrication: splash, pressure or dry-sump. Engine oil also cools and cleans.

4. Performance

• Indicated power IP = p_m L A N_c n_c / 60 (W, p_m in Pa, L in m, A in m², n_c number of cylinders, N_c power strokes per minute per cylinder = N/2 for four-stroke, N for two-stroke).
• Worked example: p_m = 6 bar, L = 0.15 m, D = 0.1 m, N = 1200 rpm, single cylinder, four-stroke: IP = 6 × 10⁵ × 0.15 × 0.007854 × 600/60 = 7069 W, about 7.07 kW.
• Brake power BP = 2πNT/60 (T in N·m). Example: T = 50 N·m at 3000 rpm gives 15.7 kW.
• Friction power FP = IP − BP. Mechanical efficiency η_m = BP/IP. Example: IP = 20 kW, FP = 4 kW gives BP = 16 kW and η_m = 80%.
• Brake thermal efficiency = BP / (m_f × CV). Example: BP = 20 kW, m_f = 0.002 kg/s, CV = 42 000 kJ/kg gives 20/84 = 23.8%.
• Brake specific fuel consumption BSFC = fuel flow per hour ÷ BP (kg/kWh). Lower is better.
• Volumetric efficiency = actual air drawn in ÷ swept volume at intake conditions.
• Methods to find friction power: Willans line (fuel against power extrapolated to zero), Morse test (cut out one cylinder at a time in multicylinder SI engines), retardation test.
• Heat balance: fuel energy goes to brake work, cooling water, exhaust gas and unaccounted losses.
• Supercharging raises intake pressure and power. Turbocharger uses exhaust gas energy; intercooling raises density.
• Emissions: carbon monoxide and hydrocarbons come from incomplete combustion; oxides of nitrogen (NOx) from high temperatures; particulate matter from diesels. A catalytic converter reduces CO, HC and NOx; exhaust gas recirculation (EGR) lowers NOx.

5. Air compressors: reciprocating

• Single-stage polytropic work (per kg or per unit): W = n/(n − 1) × p₁V₁ [(p₂/p₁)^((n−1)/n) − 1]. Isothermal work W = p₁V₁ ln(p₂/p₁). Isothermal is the minimum.
• Example: p₁ = 100 kPa, V₁ = 0.1 m³/s, p₂/p₁ = 4: isothermal W = 100 × 0.1 × ln 4 = 13.9 kW.
• Isothermal efficiency = isothermal work ÷ actual work.
• Clearance volume does not change the work per cycle on a per-unit-mass basis but reduces the volumetric efficiency: η_v = 1 + C − C (p₂/p₁)^(1/n), with C = V_c/V_s. Example: C = 0.05, pressure ratio 4, n = 1 gives 1 + 0.05 − 0.2 = 0.85.
• Higher delivery pressure lowers volumetric efficiency. At a limiting pressure ratio it falls to zero.
• Free air delivery (FAD) is the volume of air delivered, reduced to standard (intake) conditions.
• Multistage compression with intercooling: lower work, lower delivery temperature, better volumetric efficiency, smaller cylinders, lower mechanical stress, better lubrication. Minimum work when pressure ratio per stage is equal. For two stages p_i = √(p₁p₂). Example: p₁ = 1 bar, p₂ = 16 bar: p_i = 4 bar.
• Perfect intercooling: air is cooled back to the initial temperature between stages.

6. Rotary compressors

• Surging in centrifugal and axial compressors is flow reversal at low flow rates. Choking occurs at high flow when the Mach number reaches one.
• Dynamic compressors are compared by pressure ratio, flow range and isentropic efficiency.

7. Other points on engines and power plant use

• Mean effective pressure p_m is the constant pressure that, acting over one power stroke, gives the same work as the real cycle. Indicated mean effective pressure comes from the indicator diagram area divided by its length.
• Diesel generating sets are used for standby and small-station power. Large thermal and hydro stations of a power utility use turbines instead, but diesel sets back up auxiliary supplies.
• Fuel properties: calorific value (kJ/kg) is the heat released on complete combustion. Higher calorific value includes the latent heat of water vapour in the products; lower calorific value does not.
• Gas engines run on natural gas or biogas on the Otto cycle with spark ignition. Bio-diesel and ethanol blends are renewable fuels for CI and SI engines.
• Rotary (Wankel) engines have a triangular rotor and give smooth running but poor sealing.

Exam traps

• Four-stroke: one power stroke per two revolutions, so use N/2 in the IP formula.
• SI engines are throttle-governed; CI engines are governed by fuel quantity.
• Octane number is for SI fuel; cetane number is for CI fuel. Good SI fuel is a poor CI fuel.
• Compression ratio (V_s + V_c)/V_c is not swept volume ÷ clearance volume.
• Isothermal compression work is less than polytropic or adiabatic.
• Volumetric efficiency of a compressor falls as the delivery pressure rises.
• Intercooling reduces work in multistage compression but does not change the equal-ratio rule.
• Morse test applies to multi-cylinder SI engines; Willans line to CI engines.

One-liners

• 1. Four-stroke cycle: suction, compression, power, exhaust.
• 2. Swept volume = (π/4) D² L.
• 3. SI engines follow the Otto cycle; CI engines follow the Diesel cycle.
• 4. Octane scale: iso-octane 100, n-heptane 0.
• 5. Cetane scale: cetane 100, alpha-methyl naphthalene 0.
• 6. BP = 2πNT/60.
• 7. Mechanical efficiency = BP/IP.
• 8. Stoichiometric petrol air-fuel ratio is about 15:1.
• 9. Intermediate pressure for two stages p_i = √(p₁p₂).
• 10. A Roots blower has no internal compression.
• 11. Surge is flow reversal in dynamic compressors.
• 12. EGR lowers NOx.

Practice questions

1. A four-stroke engine completes one cycle in

   1. four revolutions
   2. two revolutions of the crankshaft
   3. one revolution
   4. three revolutions
   Answer

   B. two revolutions of the crankshaft

   Suction, compression, power and exhaust take two revolutions (720°).

2. In a two-stroke engine, a power stroke occurs once in every

   1. two revolutions
   2. four revolutions
   3. half revolution
   4. revolution of the crankshaft
   Answer

   D. revolution of the crankshaft

   Cycle is completed in two strokes, 360°.

3. An engine has a swept volume of 500 cc and a clearance volume of 50 cc. Its compression ratio is

   1. 9
   2. 5.5
   3. 11
   4. 10
   Answer

   C. 11

   r = (500 + 50)/50 = 11.

4. An engine has bore 0.1 m and stroke 0.12 m. The swept volume is about

   1. 942 cc
   2. 1200 cc
   3. 377 cc
   4. 94.2 cc
   Answer

   A. 942 cc

   (π/4)(0.1)²(0.12) = 9.42 × 10⁻⁴ m³.

5. A single-cylinder four-stroke engine has p_m = 6 bar, L = 0.15 m, D = 0.1 m and N = 1200 rpm. The indicated power is about

   1. 70.7 kW
   2. 7.07 kW
   3. 3.5 kW
   4. 14.1 kW
   Answer

   B. 7.07 kW

   6×10⁵ × 0.15 × 0.007854 × (1200/2)/60 = 7069 W.

6. An engine develops a torque of 50 N·m at 3000 rpm. The brake power is about

   1. 47.1 kW
   2. 15.7 kW
   3. 1.57 kW
   4. 7.85 kW
   Answer

   B. 15.7 kW

   BP = 2π × 3000 × 50/60 = 15 708 W.

7. An engine has IP = 20 kW and friction power 4 kW. The mechanical efficiency is

   1. 25%
   2. 20%
   3. 120%
   4. 80%
   Answer

   D. 80%

   BP = 16 kW; η_m = 16/20.

8. An engine develops BP = 20 kW using 0.002 kg/s of fuel of calorific value 42 000 kJ/kg. The brake thermal efficiency is about

   1. 23.8%
   2. 11.9%
   3. 42%
   4. 47.6%
   Answer

   A. 23.8%

   20/(0.002 × 42 000) = 20/84.

9. The octane number scale uses which two reference fuels?

   1. methane (100) and ethane (0)
   2. benzene (100) and toluene (0)
   3. iso-octane (100) and n-heptane (0)
   4. cetane (100) and alpha-methyl naphthalene (0)
   Answer

   C. iso-octane (100) and n-heptane (0)

   Octane number rates the knock resistance of SI fuel.

10. The cetane number scale rates

    1. viscosity of lubricating oil
    2. knock resistance of petrol
    3. the ignition quality of diesel fuel
    4. heating value of coal
    Answer

    C. the ignition quality of diesel fuel

    Higher cetane gives shorter ignition delay.

11. Knocking in a spark-ignition engine is due to

    1. very low compression ratio
    2. auto-ignition of the end gas before the flame front arrives
    3. too short an ignition delay
    4. excess lubricating oil
    Answer

    B. auto-ignition of the end gas before the flame front arrives

    The unburnt end gas detonates under high pressure and temperature.

12. Knocking in a compression-ignition engine is mainly caused by

    1. a lean mixture of petrol and air
    2. a short injection period
    3. too high a cetane number
    4. a long ignition delay followed by sudden burning of accumulated fuel
    Answer

    D. a long ignition delay followed by sudden burning of accumulated fuel

    Large fuel quantity burns at once, causing a pressure spike.

13. Statements: 1. An SI engine is governed by throttling the quantity of the mixture. 2. A CI engine is governed by varying the quantity of fuel injected. Which is/are correct?

    1. 1 only
    2. 2 only
    3. Both 1 and 2
    4. Neither 1 nor 2
    Answer

    C. Both 1 and 2

    SI: quantity governing; CI: quality governing (air is unthrottled).

14. Compared with SI engines, CI engines have

    1. a higher compression ratio
    2. a lower compression ratio
    3. a carburettor
    4. a spark plug
    Answer

    A. a higher compression ratio

    Typically 14 to 22 against 6 to 11.

15. The stoichiometric air-fuel ratio for petrol is about

    1. 40:1
    2. 15:1 by mass
    3. 100:1
    4. 5:1
    Answer

    B. 15:1 by mass

    Chemically correct mixture of air and petrol.

16. In a four-stroke engine the camshaft rotates at

    1. twice the speed of the crankshaft
    2. four times the crankshaft speed
    3. the same speed as the crankshaft
    4. half the speed of the crankshaft
    Answer

    D. half the speed of the crankshaft

    Each valve opens once in two revolutions.

17. In many small two-stroke petrol engines lubrication is provided by

    1. oil mixed with the fuel (petroil)
    2. a separate sump with pressure pump
    3. water jackets
    4. a dry-sump system
    Answer

    A. oil mixed with the fuel (petroil)

    The crankcase scavenging prevents a separate sump.

18. The Morse test is used to find the friction power of a

    1. steam turbine
    2. single-cylinder diesel engine
    3. multi-cylinder spark-ignition engine
    4. centrifugal pump
    Answer

    C. multi-cylinder spark-ignition engine

    Cylinders are cut out one by one and BP loss measured.

19. The Willans line method estimates friction power of a

    1. gas turbine by measuring torque
    2. petrol engine by cutting spark
    3. compressor by measuring flow
    4. compression-ignition engine by extrapolating the fuel consumption–power line to zero power
    Answer

    D. compression-ignition engine by extrapolating the fuel consumption–power line to zero power

    Fuel use at zero BP gives the friction power.

20. Statements: 1. Oxides of nitrogen increase with high combustion temperature. 2. Carbon monoxide results from incomplete combustion. Which is/are correct?

    1. 1 only
    2. 2 only
    3. Both 1 and 2
    4. Neither 1 nor 2
    Answer

    C. Both 1 and 2

    Both are standard facts of engine emissions.

21. Exhaust gas recirculation (EGR) is used mainly to reduce

    1. oxides of nitrogen
    2. carbon monoxide
    3. fuel consumption by 50%
    4. engine noise only
    Answer

    A. oxides of nitrogen

    Recirculated exhaust lowers peak flame temperature.

22. Supercharging an engine

    1. reduces engine speed
    2. raises the intake air pressure and increases power output
    3. lowers the intake pressure
    4. removes need for fuel
    Answer

    B. raises the intake air pressure and increases power output

    A denser charge allows more fuel to burn.

23. The ideal air-standard cycle for a spark-ignition engine is the

    1. Brayton cycle
    2. Diesel cycle
    3. Rankine cycle
    4. Otto cycle
    Answer

    D. Otto cycle

    Heat addition at constant volume.

24. Increasing the compression ratio of a petrol engine tends to

    1. increase the tendency to knock
    2. eliminate knock
    3. reduce the octane requirement
    4. reduce thermal efficiency
    Answer

    A. increase the tendency to knock

    Higher pressure and temperature favour auto-ignition of end gas.

25. For a given pressure ratio and intake state, the compression process requiring the least work is

    1. polytropic with n = 1.3
    2. isothermal compression
    3. adiabatic compression
    4. polytropic with n = 1.4
    Answer

    B. isothermal compression

    Heat removal during compression lowers work.

26. A compressor takes 0.1 m³/s of air at 100 kPa and compresses it isothermally to 400 kPa. The work rate is about

    1. 13.9 kW
    2. 40 kW
    3. 27.7 kW
    4. 10 kW
    Answer

    A. 13.9 kW

    W = p₁V₁ ln(p₂/p₁) = 100 × 0.1 × 1.386 = 13.86 kW.

27. A compressor has clearance ratio 0.05 and pressure ratio 4. For isothermal re-expansion (n = 1), the volumetric efficiency is

    1. 0.80
    2. 1.05
    3. 0.95
    4. 0.85
    Answer

    D. 0.85

    η_v = 1 + 0.05 − 0.05 × 4 = 0.85.

28. As the delivery pressure of a reciprocating compressor increases, its volumetric efficiency

    1. remains unchanged
    2. becomes more than 100%
    3. decreases
    4. increases
    Answer

    C. decreases

    Re-expansion of clearance gas occupies more of the stroke.

29. Free air delivery of a compressor is

    1. the volume of air delivered reduced to intake (atmospheric) conditions
    2. the compressor swept volume only
    3. the volume of air at delivery pressure
    4. the volume of the receiver
    Answer

    A. the volume of air delivered reduced to intake (atmospheric) conditions

    It states the actual intake capacity.

30. In a two-stage compressor with perfect intercooling, p₁ = 1 bar and p₂ = 16 bar. The intermediate pressure for minimum work is

    1. 2 bar
    2. 4 bar
    3. 15 bar
    4. 8 bar
    Answer

    B. 4 bar

    p_i = √(1 × 16) = 4 bar.

31. A two-stage air compressor takes in air at 2 bar and delivers at 18 bar. The intermediate pressure for minimum work is

    1. 8 bar
    2. 10 bar
    3. 9 bar
    4. 6 bar
    Answer

    D. 6 bar

    p_i = √(2 × 18) = 6 bar.

32. The main benefit of intercooling in a multistage compressor is

    1. higher clearance volume
    2. a reduction in compression work
    3. increased delivery temperature
    4. a higher intake temperature
    Answer

    B. a reduction in compression work

    Cooling lowers the volume at the start of the next stage.

33. Statements for a two-stage compressor with perfect intercooling and minimum work: 1. The air is cooled back to its initial temperature between the stages. 2. The work done in each stage is the same. Which is/are correct?

    1. 1 only
    2. 2 only
    3. Both 1 and 2
    4. Neither 1 nor 2
    Answer

    C. Both 1 and 2

    Equal pressure ratios and equal inlet temperatures give equal work per stage.

34. A Roots blower is a

    1. axial flow machine
    2. positive-displacement machine with no internal compression
    3. dynamic compressor with diffuser
    4. multistage reciprocating compressor
    Answer

    B. positive-displacement machine with no internal compression

    Air is trapped and pushed against delivery pressure.

35. A centrifugal compressor is a

    1. positive-displacement machine
    2. machine with sliding vanes
    3. dynamic (rotodynamic) compressor with radial flow
    4. reciprocating machine
    Answer

    C. dynamic (rotodynamic) compressor with radial flow

    Kinetic energy from the impeller is turned into pressure.

36. Axial-flow compressors are widely used in

    1. gas turbines and jet engines
    2. small air tools
    3. domestic refrigerators
    4. hand pumps
    Answer

    A. gas turbines and jet engines

    They handle very large flows efficiently.

37. Surging in a centrifugal compressor refers to

    1. leakage from the seal
    2. flow at sonic speed
    3. excess flow at high speed
    4. flow reversal and pulsations at low flow rates
    Answer

    D. flow reversal and pulsations at low flow rates

    The compressor cannot sustain the delivery pressure.

38. Brake specific fuel consumption is commonly expressed in

    1. kJ/kg
    2. kg/kWh
    3. m³/s
    4. kW/kg
    Answer

    B. kg/kWh

    Fuel mass per hour per kW of brake power.

39. In a reciprocating compressor the clearance volume mainly affects the

    1. isothermal efficiency only
    2. final temperature of the gas only
    3. volumetric efficiency
    4. speed of the shaft
    Answer

    C. volumetric efficiency

    Re-expansion reduces fresh air intake.

40. An engine has stroke 0.1 m and runs at 3000 rpm. The mean piston speed is

    1. 15 m/s
    2. 5 m/s
    3. 30 m/s
    4. 10 m/s
    Answer

    D. 10 m/s

    2LN/60 = 2 × 0.1 × 3000/60.

41. For equal size and speed, a two-stroke engine has theoretically ___ the power strokes per unit time of a four-stroke engine.

    1. twice
    2. half
    3. four times
    4. the same
    Answer

    A. twice

    One power stroke per revolution against one per two revolutions.

42. A higher cetane number of a diesel fuel gives

    1. a longer ignition delay
    2. a longer injection period
    3. higher knock tendency
    4. a shorter ignition delay
    Answer

    D. a shorter ignition delay

    Easily ignitable fuel burns smoothly.

43. In a compression-ignition engine ignition of the fuel occurs due to

    1. a spark plug
    2. a magneto
    3. the high temperature of air at the end of compression
    4. a glow of exhaust gas
    Answer

    C. the high temperature of air at the end of compression

    Air is heated by compression above the fuel's ignition temperature.

44. Out of 100 kW of fuel energy an engine gives 30 kW as brake power, 30 kW to cooling water and 33 kW to exhaust. The unaccounted loss is

    1. 3 kW
    2. 7 kW
    3. 10 kW
    4. 37 kW
    Answer

    B. 7 kW

    100 − 30 − 30 − 33 = 7 kW.

45. A catalytic converter on a petrol engine mainly converts

    1. CO, HC and NOx into less harmful gases
    2. CO₂ into CO
    3. water into steam
    4. nitrogen into oxygen
    Answer

    A. CO, HC and NOx into less harmful gases

    A three-way catalyst oxidises CO and HC and reduces NOx.