Combustion in CI engines: delay period and cetane number

The four stages of CI combustion, what sets the ignition delay and causes diesel knock, and how cetane number rates a fuel's ignition quality, with delay calculations.

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Why it matters

A diesel engine has no spark: combustion starts only when the injected fuel ignites by itself in hot compressed air. The time this takes, the delay period, decides how much fuel has piled up in the cylinder before burning begins, and so sets the rate of pressure rise, diesel knock, noise, NOx and cold-start behaviour. Cetane number is the fuel property that controls it, which is why it appears in every diesel fuel specification.

Key ideas

Stages of CI combustion. Plotting cylinder pressure against crank angle, four stages are recognised:

  1. Ignition delay period – from the start of injection to the start of combustion (the point where the pressure curve departs from the motoring curve). Fuel is being injected throughout but nothing burns yet.
  2. Period of rapid (uncontrolled, premixed) combustion – the fuel that accumulated and mixed during the delay burns almost at once, giving a steep pressure rise. Its intensity depends directly on the length of the delay.
  3. Period of controlled (mixing-controlled) combustion – the fuel still being injected burns about as fast as it can mix with air; the rate is controlled by injection rate and air motion. Peak pressure and temperature occur here.
  4. After-burning – fuel left unburned (and soot) continues to burn during expansion; a long after-burning period wastes energy and raises exhaust temperature and smoke.

Physical and chemical delay. The delay is the sum of a physical delay (atomisation, evaporation, mixing of the fuel with air, and raising it to air temperature) and a chemical delay (pre-flame reactions that lead to auto-ignition). They overlap; at normal operating temperatures the chemical delay usually dominates. Typical delays in warm engines are of the order of 0.5–2 ms.

Diesel knock. If the delay is long, a large quantity of fuel is in the chamber, well mixed, when ignition occurs. It burns almost instantaneously, giving a very high rate of pressure rise and a sharp knocking noise. So diesel knock is caused by too long a delay, i.e. by fuel that is too reluctant to auto-ignite – exactly the opposite of SI knock, where the problem is end gas that auto-ignites too easily. Diesel knock originates at the start of combustion, SI knock at the end.

Factors affecting the delay period (and therefore diesel knock):

  • Compression ratio ↑ → higher air temperature and pressure at injection → delay ↓.
  • Intake temperature and pressure ↑ (supercharging, turbocharging, hot coolant) → delay ↓. Cold starting is hard because the delay becomes very long.
  • Load ↑ → hotter walls and residual gas → delay ↓.
  • Engine speed ↑ → delay in milliseconds falls slightly (better turbulence, less heat loss), but delay in crank degrees increases because the crank turns faster; injection must be advanced with speed.
  • Injection timing – injecting too early (air still cool) or too late lengthens the delay; minimum delay is a little before TDC.
  • Atomisation and air motion – higher injection pressure, finer droplets and good swirl shorten the physical delay.
  • Fuel – higher cetane number shortens the chemical delay; volatility and viscosity affect the physical delay.

Remember the summary: the conditions that reduce diesel knock (high compression ratio, hot dense air, high cetane fuel) are the conditions that cause SI knock.

Cetane number. Ignition quality is rated in a standard CFR diesel engine against reference fuels. The primary references are n-cetane (n-hexadecane, CN 100, ignites readily) and α-methylnaphthalene (CN 0, poor ignition quality). The cetane number of a fuel is the percentage by volume of n-cetane in the blend that gives the same delay under standard conditions. Today the low reference is usually heptamethylnonane (HMN), which has CN 15, so a blend of x% n-cetane and (100 − x)% HMN has CN = x + 0.15(100 − x).

  • Market diesel in India must meet a minimum cetane number of about 51 (check the current IS 1460 table).
  • Too high a cetane number is not better: ignition occurs before good mixing and smoke can rise.
  • Cetane improvers (for example 2-ethylhexyl nitrate) shorten the delay.
  • The cetane index is a calculated estimate from density and distillation temperatures, used where engine testing is not practical; the diesel index = API gravity × aniline point (°F) / 100 is an older correlation.
  • Straight-chain paraffins have high CN and low ON; aromatics have low CN and high ON. A good diesel fuel is a poor petrol and vice versa.

Connection to neighbouring topics. Injection timing, pilot injection and rail pressure (fuel injection topic) are the main tools for controlling the delay; chamber design and swirl (next topic) control the mixing-controlled phase; the premixed-burn spike is a major NOx source.

Formulas

τ_crank = 6 × N × τ

  • τ_crank = delay in crank angle degrees; N = engine speed (rev/min); τ = delay (s).

CN = x_C + 0.15 × x_HMN

  • CN = cetane number; x_C = volume percentage of n-cetane; x_HMN = volume percentage of heptamethylnonane in the matching blend.

T₂ = T₁ × r^(n−1) and p₂ = p₁ × r^n

  • Air temperature (K) and pressure at the end of compression for polytropic compression with index n; r = compression ratio. Gives the conditions the fuel meets at injection.

τ = A × p^(−m) × exp(E / (R_u × T))

  • Empirical Arrhenius-type delay correlation; A, m and E/R_u are constants fitted to experiments. One classic form (Wolfer) is τ = 0.44 × p^(−1.19) × exp(4650 / T) with τ in ms, p in atm, T in K. Use the constants your data book gives; they apply to a limited range.

Worked examples

Example 1 (standard): delay in crank degrees and a reference blend. (a) A diesel engine runs at 2400 rev/min with a delay of 1.0 ms and injection starting 18° before TDC. When does combustion start? (b) A fuel matches a blend of 60% n-cetane and 40% heptamethylnonane. Find its cetane number.

  1. τ_crank = 6 × N × τ = 6 × 2400 × 1.0 × 10⁻³ = 14.4°.
  2. Start of combustion = 18° − 14.4° = 3.6° before TDC.
  3. CN = x_C + 0.15 × x_HMN = 60 + 0.15 × 40 = 66.

Answer: (a) combustion starts at about 3.6° bTDC; (b) CN = 66.

Example 2 (GATE level): effect of turbocharging on delay. A diesel engine has r = 18. Compression is polytropic with n = 1.35. Use τ = 0.44 × p^(−1.19) × exp(4650/T) (τ in ms, p in atm, T in K) at the end-of-compression state. Compare (a) naturally aspirated, inlet 1.0 bar and 310 K, with (b) turbocharged and intercooled, inlet 1.8 bar and 330 K. Express each delay in crank degrees at 2000 rev/min.

  1. r^(n−1) = 18^0.35 = 2.750; r^n = 18^1.35 = 49.50.
  2. (a) T₂ = T₁ × r^(n−1) = 310 × 2.750 = 852.5 K; p₂ = p₁ × r^n = 1.0 × 49.50 = 49.50 bar = 48.85 atm.
  3. τ = 0.44 × 48.85^(−1.19) × exp(4650/852.5) = 0.44 × 0.009777 × exp(5.454) = 0.44 × 0.009777 × 233.8 = 1.006 ms.
  4. Crank angle = 6 × 2000 × 1.006 × 10⁻³ = 12.1°.
  5. (b) T₂ = 330 × 2.750 = 907.5 K; p₂ = 1.8 × 49.50 = 89.10 bar = 87.94 atm.
  6. τ = 0.44 × 87.94^(−1.19) × exp(4650/907.5) = 0.44 × 0.004858 × 168.0 = 0.359 ms.
  7. Crank angle = 6 × 2000 × 0.359 × 10⁻³ = 4.3°.

Answer: (a) τ ≈ 1.01 ms ≈ 12.1°; (b) τ ≈ 0.36 ms ≈ 4.3°. Boosting shortens the delay sharply, which is why turbocharged diesels run more quietly and are less prone to diesel knock.

Common mistakes

  • Saying a long delay helps mixing and therefore lowers knock. A long delay causes diesel knock because more fuel burns in the premixed spike.
  • Transferring SI rules to CI engines: a higher compression ratio or hotter intake reduces diesel knock.
  • Forgetting that HMN has CN 15, not 0, when finding cetane number from a blend.
  • Assuming delay in degrees falls with engine speed; in milliseconds it falls slightly, in degrees it rises.
  • Calling cetane number "the diesel equivalent of octane number" without noting that they rate opposite properties: high CN means easy auto-ignition, high ON means resistance to it.
  • Using bar in a correlation written for atm, or °C instead of K in the exponential.

For GATE ME

Expect conceptual questions on the four stages of CI combustion, the cause of diesel knock, the effect of compression ratio, intake conditions, speed and load on the delay, and the contrast between SI and CI knock factors. Numericals ask for the delay in crank degrees, the start of combustion from injection timing, cetane number from a reference blend, and end-of-compression temperature and pressure feeding a given delay correlation. Practise the SI-versus-CI factor table and the time-to-crank-angle conversion.

Quick check

  1. Name the four stages of combustion in a CI engine.
  2. Does increasing the compression ratio increase or decrease diesel knock?
  3. A delay of 1.5 ms at 1800 rev/min equals how many crank degrees?
  4. Which reference fuel has cetane number 100?
  5. Why do diesel engines knock more when started cold?

Answers: 1. Ignition delay, rapid (premixed) combustion, controlled combustion, after-burning; 2. Decrease; 3. 6 × 1800 × 1.5 × 10⁻³ = 16.2°; 4. n-cetane (n-hexadecane); 5. Cold air and walls lengthen the delay, so more fuel accumulates before ignition.

Interview questions

All Automotive Engines, Emissions and Alternate Fuels interview questions

Try answering each one aloud before you open it.

  1. 1.What is the delay period in a compression ignition (CI) engine?Concept

    It is the interval between the start of injection and the start of combustion, seen as the point where the cylinder pressure rises above the motoring curve. It has a physical part (atomisation, evaporation and mixing of fuel with hot air) and a chemical part (pre-flame reactions leading to auto-ignition), which overlap. In a warm engine it is typically of the order of 0.5 to 2 ms. Its length matters because all the fuel injected during the delay burns at once when ignition occurs, which sets the rate of pressure rise, noise and NOx.

  2. 2.Explain the significance of the cetane number in diesel fuels.Concept

    Cetane number rates a diesel fuel's ignition quality, that is how readily it auto-ignites, and therefore how short its ignition delay is. It is the volume percentage of n-cetane (CN 100) in a blend with α-methylnaphthalene (CN 0), or with heptamethylnonane (CN 15) in the modern method, that gives the same delay in a standard CFR engine. Higher CN gives easier cold starting, less diesel knock and lower noise. It rates the opposite property to octane number: a high-cetane fuel auto-ignites easily, a high-octane fuel resists it.

  3. 3.How does the delay period affect the performance of a CI engine?Application

    During the delay fuel keeps being injected and mixing with air without burning. When ignition finally occurs, this accumulated fuel burns almost at once in the premixed phase, so a longer delay gives a higher rate of pressure rise, harder combustion noise (diesel knock), higher peak temperature and more NOx, and higher mechanical loads. A very short delay gives smooth combustion but leaves more fuel to burn in the mixing-controlled phase, which can raise smoke. Engines are calibrated, often with a pilot injection, to keep the delay short but controlled.

  4. 4.Why is a high cetane number preferred in cold climates?Application

    In cold weather the intake air, cylinder walls and fuel are cold, so the air temperature at the end of compression is lower and the ignition delay becomes much longer. A low-cetane fuel may then fail to ignite at all during cranking, or ignite late with heavy knock and white smoke of unburned fuel. A higher cetane number shortens the chemical delay, giving quicker, more reliable starting and smoother warm-up.

  5. 5.What happens if a diesel engine uses fuel with a low cetane number?Application

    Using fuel with a low cetane number can lead to longer ignition delays, resulting in rough engine operation, increased noise, and higher emissions. It may also cause starting difficulties, especially in cold weather, and can lead to engine knocking.

  6. 6.Describe the relationship between cetane number and engine knocking in CI engines.Concept

    In a CI engine knock is caused by a long ignition delay: fuel injected during the delay accumulates and then burns almost instantaneously, producing a very steep pressure rise and the characteristic knocking noise at the start of combustion. A low-cetane fuel lengthens the delay and so increases diesel knock, while a high-cetane fuel shortens it. This is the opposite of SI engines, where knock is auto-ignition of the end gas at the end of combustion and is caused by fuel that ignites too easily.

  7. 7.How can the delay period be minimized in a CI engine?Application

    Raise the temperature and pressure of the air at injection: higher compression ratio, supercharging or turbocharging, warmer intake air and coolant, and higher load all shorten the delay. Inject at the right point, slightly before TDC, since injecting too early or too late lengthens it. Improve the physical part with higher injection pressure, finer atomisation and good swirl, and use a fuel with higher cetane number or a cetane improver. Modern engines also use a small pilot injection so that the main injection meets already burning gas and has a very short delay.

  8. 8.Calculate the cetane number of a diesel fuel blend containing 60% of a fuel with a cetane number of 50 and 40% of a fuel with a cetane number of 70.Numerical

    As a first approximation cetane number blends linearly by volume, so CN ≈ 0.60 × 50 + 0.40 × 70 = 30 + 28 = 58. Real fuels do not blend exactly linearly, especially when cetane improvers or very different hydrocarbon types are mixed, so the blend should be checked by an engine test or a cetane index calculation when it matters. The key is to weight by volume fraction, not to average the two numbers.

  9. 9.If the delay period in a CI engine is 2 milliseconds, and the engine speed is 1500 RPM, how many crankshaft degrees does the delay period correspond to?Numerical

    First, calculate the time for one revolution: 1500 RPM = 25 revolutions per second, so one revolution takes 1/25 seconds = 40 milliseconds. Since one revolution is 360 degrees, 2 milliseconds corresponds to (2/40) * 360 = 18 degrees of crankshaft rotation.

  10. 10.What are the potential environmental impacts of using diesel fuels with low cetane numbers?Application

    A low cetane number lengthens the ignition delay, so more fuel burns in the premixed spike, which raises peak temperature and NOx and increases combustion noise. At cold start and light load the fuel may ignite late or partially, giving white smoke and high unburned hydrocarbon and CO emissions, and in older engines more smoke. Higher NOx and HC add to smog and ozone formation and to health effects, which is why fuel standards specify a minimum cetane number.

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